LT 

ro 


1862. 


IN  MEMORIAM. 

John  Swett 


THE 


PROGRESSIVE 

PRIMARY    ARITHMETIC, 

FOB  PRIMARY  CLASSES 
PUBLIC  AND  PEIVATE  SCHOOLS. 


BY 

HORATIO  N.  ROBINSON,  LL.  D. 

AUTHOR  OP  A  FULL  COURSE  OF  MATHEMATICS. 


NEW    YORK: 

IYISON,  PHINNEY  &  CO.,  48  &  50  WALKER  ST. 

CHICAGO  :  S.  C.  GRIGGS  &  CO.,  39  &  41  LAKE  ST. 

BOSTON:  BROWN,  TAOGAKD  &  CHASE.    PHILADELPHIA.:  SOWER,  BARXKS 

it,  CO.,  AND  J.  B.  LIPPINOOTT  A  CO.    CINCINNATI:  MOOKK.  \VILSTACH, 

KKY8  A  CO.    SAVANNAH  :  J.  M.  COOPKK  A  CO.    ST.  LOUIS  :  KE1TU 

tt  WOODS.    KKW  ORLKANS:  BLOOMFIKLD,  STKEL  A  CO. 

DETROIT:  F.  RAYMOND  A  co. 

1862. 


Entered,  according  to  Act  of  Congress,  in  the  year  1858,  by 
DANIEL  W.  FISH,  A.M. 

In  the  Clerk's  Office  of  the  District  Court  of  the  United  States  for 
Northern  New  York. 


<•       •.;- 


ELECTROTTPED  AT    THE 
BOSTON     STEREOTYPE     FOUNDRY. 


PEEFACE. 


THIS  primary  work  is  designed  for  small  children, 
and  as  an  easy  introduction  to  the  "  Progressive  Intel- 
lectual Arithmetic,"  for  advanced  classes. 

Its  object  is  to  lead  the  young  pupil,  by  brief  and 
simple  processes,  applied  to  practical  examples  of  easy 
gradation,  to  acquire  habits  of  thought  and  of  reasoning, 
in  their  simplest  forms,  and  to  draw  out  and  strengthen 
the  mind  by  a  progressive  and  almost  imperceptible  gra- 
dation of  thought  and  expression. 

The  operations  of  Adding  and  Subtracting,  of  Multi- 
plying and  Dividing,  are  first  shown  by  pictorial  objects ; 
portions  of  the  elementary  tables  are  introduced  at  the 
commencement  of  each  lesson,  and  applied  to  short  ex- 
amples concerning  familiar  objects ;  promiscuous  reviews 
of  the  elementary  tables,  and  the  more  simple  and  easy 
Denominate  tables  have  been  introduced.  Fractions 
have  been  treated  as  far  as  was  thought  practicable 
in  a  work  of  this  kind. 

It  gives  me  pleasure  to  acknowledge  my  obligations 
toD.  W.Fish.  A.M.,  of  Rochester,  N.  Y.,  a  thorough,  prac- 
tical teacher,  and  who  has,  by  my  request,  prepared  this 
little  book,  which,  it  is  confidently  believed,  will,  by  its 
progressive  and  systematic  arrangement,  its  simplicity 
and  adaptation  to  the  juvenile  mind,  insure  for  it  abun- 
dant success. 

54!?3t  ,3, 


SUGGESTIONS  TO  TEACHERS. 


1.  A  TEACHER  should  have  a  particular  time  allotted 
to  every  exercise,  and  regular  lessons  should  be  assigned, 
to  be  recited  each  day  at  a  specified  hour. 

2.  Sufficient  time  being  given  the  pupils  to  learn 
their  lessons,  they  should  not  be  allowed  the  use  of  the 
book  at  the  time  of  recitation. 

3.  The  teacher  should  first  ascertain  that  the  table  is 

4» 

thoroughly  learned  by  every  pupil  in  the  class. 

4.  Each  question  should  be  slowly  and  distinctly  read, 
and  the  pupils  be  called  upon  promiscuously ;  the  pupil 
called  upon  should  stand  erect,  repeat  the  question,  and 
then  give  the  solution.     This  will  require  close  attention. 

5.  A  correct  and  uniform  analysis  of  each  question 
should  be  required  from  every  pupil. 

6.  The  class  should  be  encouraged  to  detect  and  cor- 
rect errors  in  the  statement  and  solution  of  questions,  to 
be  signified  by  raising  the  hand. 

7.  The  teacher  can  extend  the  questions  in  each  les- 
son at  pleasure,  either  by  repeating   those   given,  or 
making  additional  ones. 

(4) 


PRIMARY  ARITHMETIC. 


LESSON    I. 

1.  What  is  the  first  thing  to  be  taught  and  learned  in  Arith- 

metic?    ANS.  Counting. 

2.  What  is  counting  ?     ANS.  Expressing  numbers  by  words. 

3.  What  is  a  number  r     ANS.  A  unit,  or  a  collection  of  units. 

4.  What  is  a  unit  ?     ANS.  A  single  thing. 

5.  How  may  numbers  be  expressed  ?     ANS.  By  words,  letters, 

and  figures. 

6.  Which  is  the  most  common  method?     ANS.  By  figures. 

7.  How  many  figures  are  used  to  express  numbers  ?    ANS.  Ten. 

8.  Name  them. 

ANS.  Naught,  One,  Two,  Three,  Four,  Five,  Six,  Seven,  Eight,  Nine. 
0,          1,       2,       3,         4,       5,      6,       7,         8,        9. 


9.  Count  the  bells  on  each  of  the  above  rows. 


NOTATION   AND   NUMERATION. 


LESSON     II. 

1.  What  is  No tation?    Ans.  Writing ^  num- 
bers. 

2.  What  is  Numeration  ?     Ans.   Reading 
numbers. 

3.  How  many  letters  are  used  to  express 
numbers  ?     Ans.    Seven. 

4.  What  are  they?     Ans.   I,  V,  X,  L,  C, 
D,  and  M. 

5.  What  is  this  method  called  ?    Ans.  The 
Roman  method. 

6.  Why  is  it  so  called?     Ans.  Because  it 
was  first  used  by  the  Romans. 

7.  How  many  figures  or   characters   are 
used  to  express  numbers  ?     Ans.    Ten. 

8.  What  are  they  ?     Ans.    0, 1,  2,  3,  4,  5, 
6,  7,  8,  9. 

9.  What   is  this   method   called?     Ans. 
The  Arabic  method. 

10.  Why  is  it  so  called?     Ans.   Because 
it  was  first  used  by  the  Arabs. 

11.  What  may  the  ten  figures  used  in  ex- 
pressing  numbers    be   called?      Ans.   The 
Arithmetical  Alphabet. 

12.  Can  all  numbers  be  expressed  by  these 
ten  figures  ?     Ans.    They  can,  by  repeating 
and  combining  them. 


NOTATION   AND   NUMERATION. 

7 

LE 

SSON   III. 

REMARK.  —  This   lesson  presents   the   printed   and 
written  figures,  and  the  Roman  letters,  by  which  num- 
bers are  commonly  expressed.     It  should  be  carefully 
studied  by  children,  until  they  can  read  the  figures  with 
facility  when  written  on  the  black-board,  or  when  they 
meet  with  them  in  books. 

Numbers. 

Printed               Written 
Figures.              Figures. 

Roman 

Letters. 

Naught 

0                  o 

One 

i             / 

I 

Two 

2                   2 

II 

Three 

3                s 

III 

Four 

4                  4 

IV 

Five 

5                   5 

V 

Six 

6                6      " 

VI 

Seven 

7                 / 

VII 

Eight 

8                 $ 

VIII 

Nine 

9                 9 

^IX 

Ten 

10                40 

X 

Eleven 

11               // 

XI 

Twelve 

12               42 

XII 

Thirteen 

13                43 

XIII 

Fourteen 

14               44 

XIV 

Fifteen 

15                  45 

XV 

Sixteen 

16                 46 

XVI 

Seventeen 

17                // 

XVII 

Eighteen 

18               4$ 

XVIII 

Nineteen 

19                49 

XIX 

Twenty 

20                go 

XX 

Twenty-one 

21               34 

XXI 

8                      NOTATION  AND  NUMERATION. 

L 

ESS 

ON    IV. 

Numbers. 

Printed 
Figures 

Written 
Figures. 

Roman 

Letters. 

Twenty-two 

22 

22 

XXII 

Twenty-three 

23 

S3 

XXIII 

Twenty-four 

24 

24 

XXIV 

Twenty-five 

25 

25 

XXV 

Twenty-six 

26 

26 

XXVI 

Twenty-seven 

27 

27 

XXVII 

Twenty-eight 

2$ 

2$ 

XXVIII 

Twenty-nine 

29 

29 

XXIX 

Thirty 

3t 

30 

XXX 

Thirty-one 

81 

Sf 

XXXI 

Forty 

40 

40 

XL 

Forty-one 

41 

4tf 

XLI 

Fifty 

50 

50 

L 

Fifty-one 

51 

5f 

LI 

Sixty 

60 

60 

LX 

Sixty-one 

61 

6S 

LXI 

Seventy 

70 

70 

LXX 

Seventy-one 

71 

rt 

LXXI 

Eighty 

89 

$0 

LXXX 

Eighty-one 

81 

$s 

LXXXI 

Ninety 

9$ 

90 

XC 

Ninety-one 

91 

9* 

XCI 

Ninety-two 

92 

92 

XCII 

One  hundred 

10d 

too 

C 

Two  hundred 

200 

200 

CC 

Five  hundred 

500 

500 

D 

One  thousand 

10©0 

4000 

M 

NOTATION  AND  NUMERATION. 


LESSON  V. 

REMARK.  —  The  children  should  now  be  furnished 
with  slates  and  pencils,  and  required  to  read  the  follow- 
ing numbers  from  the  book,  or  when  written  on  the 
black-board  by  the  teacher,  and  then  to  copy  them  on 
their  slates  in  straight  columns. 

1  11  21  31  41 

2  12  22  32  42 

3  13  23  33  43 

4  14  24  34  44 

5  15  25  35  45 

6  16  26  36  46 

7  17  27  37  47 

8  18  28  38  48 

9  19  29  39  49 
10  20  30  40  50 


LESSON  VI. 

51  61  71  81  91 

52  62  72  82  92 

53  63  73  83  93 

54  64  74  84  94 

55  65  75  85  95 

56  66  76  86  96 

57  67  77  87  97 

58  68  78  88  98 

59  69  79  89  99 

60  70  80  90  100 


10 


ADDITION. 


LESSON    I. 

Putting  two  or  more  numbers  or  things  together  into 
one  sum,  is  called  ADDITION  :  thus, 


1. 


m  and  m  more  make 

^g.          ^£  ^g,  ^ 

mug         mug  mugs. 


2. 


and 


IS  more  make 


tree 


trees 


2  2 

3.     C^<^  and  <£^£&  more  make 
caps  caps 


6. 


trees. 
4 


ADDITION.  11 


LESSON    II. 


1  and  1  are  2 
1  and  2  are  3 
1  and  3  are  4 
1  and  4  are  5 
1  and  5  are  6 


1  and     6  are  7 

1  and     7  are  8 

1  and  ,  8  are  9 

1  and     9  are  10 

1  and  10  are  11 


1.  If  a  slate  pencil  cost  1  cent,  and  an  or- 
ange 3  cents,  how  many  cents  will  both  cost  ? 

ANALYSIS.  —  They  will  both  cost  as  many  cents  as  the 
sum  of  1  cent  and  3  cents,  which  is  4  cents.  Therefore 
if  a  slate  pencil  cost  1  cent,  and  an  orange  3  cents,  they 
will  both  cost  4  cents. 

2.  Sarah  had  4  books,  and  her  mother 
gave  her  1  more ;  how  many  books  did  she 
then  have  I 

3.  In  a  garden  are  1  plum  tree  and  6  pear 
trees  ;  how  many  trees  in  the  garden  ? 

4.  A  man  gave  8  dollars  for  a  coat,  and  1 
dollar  for  a  hat ;  how  much  did  he  give  for 
both? 

5.  In  a  class  are  5  girls  and  1  boy ;  how 
many  pupils  in  the  class  ? 

6.  A  boy  gave  1  cent  for  a  sponge,  and  10 
cents  for  a  spelling  book ;  what  did  he  give 
for  both? 

7.  Bought  a  broom  for  1  shilling,  and  some 
sugar  for  9  shillings ;  what  did  both  cost  ? 


12  ADDITION. 


LESSON    III. 


2  and  1  are  3 
2  and  2  are  4 
2  and  3  are  5 
2  and  4  are  6 
2  and  5  are  7 


2  and  6  are  8 
2  and  7  are  9 
2  and  8  are  10 
2  and  9  are  11 
2  and  10  are  12 


1.  James  rode  2  miles  in  the  stage,  and  4 
miles  in  the  cars;  how  far  did  he  ride  in 
both? 

ANALYSIS.  —  He  rode  as  many  miles  as  the  sum  of 
2  miles  and  4  miles,  which  is  6  miles.  Therefore,  since 
James  rode  2  miles  in  the  stage  and  4  miles  in  the  cars, 
he  rode  6  miles  in  both. 

2.  If  a  barrel  of  cider  cost  2  dollars,  and  a 
barrel  of  flour  7  dollars,  what  will  both  cost  ? 

3.  A  man  had  2  sons  and  5  daughters  to 
support ;  how  many  children  had  he  ? 

4.  A  lady  gave  2  cents  for  some  ribbon, 
and  10  cents  for  a  comb;  what  did  she  pay 
for  both  ? 

5.  A  farmer  sold  a  sheep  for  2  dollars,  and 
a  hog  for  9  dollars ;  what  did  he  get  for  both  ? 

6.  John  went  to    the  river  to  fish,  and 
caught  2  trout  and  8  perch ;  how  many  fish 
did  he  catch  ? 

7.  If  a  boy  spend  2  cents  and  have  2  left, 
how  many  cents  had  he* at  first? 


ADDITION.  13 


LESSON    IV, 


3  and  1  are  4 
3  and  2  are  5 
3  and  3  are  6 
3  and  4  are  7 
3  and  5  are  8 


3  and  6  are  9 
3  and  7  are  10 
3  and  8  are  11 
3  and  9  are  12 
3  and  10  are  13 


1.  Frank  picked  3  ripe  plums  from  one 
tree,  and  5  from  another ;  how  many  did  he 
pick  from  both  ? 

ANALYSIS.  —  As  many  plums  as  the  sum  of  3  plums 
and  5  plums,  which  is  8  plums.  Therefore,  since  Frank 
picked  3  plums  from  one  tree,  and  5  from  another,  he 
picked  8  plums  both. 

2.  A  grocer  sold  3  pounds  of  sugar  to  one 
man,  and  4  to  another;  how  many  pounds 
did  he  sell  to  both  1 

3.  Mary  bought  an  inkstand  for  7  cents, 
and  some  paper  for  3  cents ;  how  much  did 
she  pay  for  both  ? 

4.  A  beggar  received  6  cents  from  one  lit- 
tle girl,  and  3  from  another ;  how  many  cents 
did  he  receive  from  both  ? 

5.  A  boy  found  two  hen's  nests ;  in  one 
were  8  eggs,  in  the  other  3  eggs ;  how  many 
eggs  were  there  in  both  nests  ? 

6.  A  knife  cost  9  cents,  and  a  top  3  cents ; 
what  did  they  both  cost  I 


14  ADDITION. 


LESSON   V. 


4  and  1  are  5 
4  and  2  are  6 
4  and  3  are  7 
4  and  4  are  8 
4  and  5  are  9 


4  and  6  are  10 
4  and  7  are  11 
4  and  8  are  12 
4  and  9  are  13 
4  and  10  are  14 


1.  Henry  had  4  cents  in  one  hand  and  3 
cents  in  the  other ;  how  many  cents  had  he 
in  both  ? 

ANALYSIS.  —  As  many  cents  in  both  as  the  sum  of  4 
cents  and  3  cents,  which  is  7  cents.  Therefore,  since 
Henry  had  4  cents  in  one  hand,  and  3  cents  in  the  other, 
he  had  7  cents  in  both. 

2.  If  a  skein  of  silk  cost  4  cents,  and  a 
yard  of  tape  6  cents,  how  much  do  both  cost? 

3.  A  farmer  has  4  black   sheep,  and  8 
white  ones ;  how  many  sheep  has  he  of  both 
kinds  ? 

4.  There  are  5  birds  on  one  tree,  and  4  on 
another ;  how  many  birds  are  there  on  both 
trees  ? 

5.  Rollin  had  4  books,  and  his  father  gave 
him  4  more ;  how  many  books  had  he  then  ? 

6.  If  a  lady  paid  7  dollars  for  a  dress,  and 
4  for  a  bonnet,  what  did  she  pay  for  both  1 

7.  There  are  4  books  on  one  shelf,  and  9  on 
another ;  how  many  books  on  both  shelves  1 


ADDITION.                                         15 

LESS< 

5  and  1  are     6 
5  and  2  are     7 
5  and  3  are     8 
5  and  4  are     9 
5  and  5  are  10 

3N   VI. 

5  and     6  are  11 
5  and     7  are  12 
5  and     8  are  13 
5  and     9  are  14 
5  and  10  are  15 

1.  A  miller  sold  5  barrels  of  flour  at  one 
time,  and  4  barrels  at  another;  how  many 
barrels  did  he  sell  in  all  1 

2.  George  lost  2  cents,  and  had  5  cents 
left ;  how  many  cents  had  he  at  first  ? 

3.  Gave  5  cents  for  a  writing  book,  and 
3  cents  for  a  pen  holder ;  what  was  the  cost 
of  both? 

4.  A  boy  had  7  peaches  in  his  basket,  and 
his  sister  put  in  5  more ;  how  many  peaches 
had  he  then  ? 

5.  Joseph   rode    6  miles,  and   walked  5 
miles ;  how  far  did  he  go  1 

6.  Carrie  had  5  roses,  and  Nellie  had  8 ; 
how  many  roses  had  both  ? 

7.  A  merchant  sold  5  yards  of  calico  at 
one  time,  and  5  at  another ;  how  many  yards 
did  he  sell  in  all  I 

8.  A  farmer  paid  10  dollars  for  a  plow,  and 
5  dollars  for  a  harrow ;  how  much  did  he  pay 
for  both  1 


16  ADDITION. 


LESSON   VII. 


6  and  1  are  7 

6  and  2  are  8 

6  and  3  are  9 

6  and  4  are  10 

6  and  5  are  11 


6  and  6  are  12 
6  and  7  are  13 
6  and  8  are  14 
6  and  9  are  15 
6  and  10  are  16 


1.  A  boy,  after  losing  6  marbles,  had  4 
left ;  how  many  had  he  at  first  \ 

2.  Albert  spent  6  cents,  and  had  5  left ; 
how  many  had  he  at  first  ? 

3.  A  man  paid  3  dollars  for  a  barrel  of 
cider,  and  6  dollars  for  a  barrel  of  flour; 
what  did  he  pay  for  both  1 

4.  A  gardener  picked  6  peaches  from  one 
tree,  and  7  from  another ;  how  many  peaches 
did  he  pick  from  both  ? 

5.  Dick  caught  2  gray  squirrels,  and  6 
red  ones ;  how  many  did  he  catch  in  all  1 

6.  A  cabinet  maker  asks  6  dollars  for  a 
rocking  chair,  and  6  dollars  for  a  table ;  what 
is  the  cost  of  both  ? 

7.  In  the  fruit  dish  are  6  red  apples  and 
9  green   ones ;    how   many   apples   in   the 
dish  \ 

8.  Edwin  is  6  years  old,  and  his  sister 
Martha  is  10  years  older ;  what  is  the  age 
of  .Martha? 


ADDITION.  17 


LESSON   VIII. 


7  and  1  are     8 

7  and  2  are     9 

7  and  3  are  10 

7  and  4  are  11 

7  and  5  are  12 


7  and  6  are  13 
7  and  7  are  14 
7  and  8  are  15 
7  and  9  are  16 
7  and  10  are  17 


1.  Bought  a  ton  of  hay  for  7  dollars,  and 
some  oats  for  6  dollars ;  what  was  the  cost 
of  both  1 

2.  David  gathered  3  quarts  of  walnuts, 
and  Homer  7  quarts ;  how  many  quarts  did 
both  gather  ? 

3.  Howard  had  7  rabbits,  and  Herbert 
gave  him  2  more ;  how  many  had  he  then  ? 

4.  A  farmer  picked  5  bushels  of  apples 
from  one  tree,  and  7  bushels  from  another ; 
how  many  bushels  did  he  gather  from  both  ? 

5.  Asa  is  8  years  old ;  how  old  will  he  be 
7  years  from  this  time  ? 

6.  In  a  basket  are  7  bunches  of  green 
grapes  and  7  bunches  of  purple  ones ;  how 
many  bunches  of  both  ? 

7.  If  a  boy  earn  7  shillings  in  one  week, 
and  9  shillings  the  next,  how  many  shillings 
will  he  earn  in  2  weeks  1 

8.  In  a  shop,  2  men  and  7  boys  are  em- 
ployed ;  how  many  persons  are  employed  ? 


18  ADDITION. 


LESSON    IX, 


8  and  1  are  9 
8  and  2  are  10 
8  and  3  are  11 
8  and  4  are  12 
8  and  5  are  13 


8  and  6  are  14 
8  and  7  are  15 
8  and  8  are  16 
8  and  9  are  17 
8  and  10  are  18 


1.  Henry  hoed  8  rows  of  corn  one  day, 
and  5  the  next ;  how  many  rows  did  he  hoe 
in  both  days  ] 

2.  Andrew  had  8  apples  and  8  peaches  in 
his  basket ;  how  many  had  he  of  both  ? 

3.  There  are  3  gentlemen  and  8  ladies  in 
a  boat ;  how  many  persons  in  the  boat  ? 

4.  A  man  had  8  dollars,  and  borrowed  6 
more ;  how  many  dollars  had  he  then  ? 

5.  Bought  a  pound  of  raisins  for  9  cents, 
and  a  pound  of  sugar  for  8  cents ;  what  was 
the  cost  of  both  ? 

6.  Emily  had  7  white  roses  and  8  red 
ones;    how  many   roses   had   she   of  both 
kinds? 

7.  A  boy  sold  8  boxes  of  matches  to  one 
man,  and  4  boxes   to  another;  how  many 
boxes  did  he  sell  to  both  ? 

8.  There  are  10  shade  trees  now  in  the 
park,   and    8   have  been  cut  down;     how 
many  trees  were  set  out  ? 


ADDITION.  19 


LESSON   X. 


9  and  1  are  10 
9  and  2  are  11 
9  and  3  are  12 
9  and  4  are  13 


9  and  6  are  15 

9  and  7  are  16 

9  and  8  are  17 

9  and  9  are  18 


9  and  5  are  14        9  and  10  are  19 


1.  If  a  firkin  of  butter  is  worth  0  dollars, 
and  a  cord  of  wood    '  dollars,  what  are  both 
worth  ? 

2.  A  lady  bought  a  muff  for  9  dollars, 
and  a  hat  for  5  dollars;  what  did  she  pay 
for  both  ? 

3.  Cora  read  10  pages  of  history,  and  9 
pages  of  poetry;  how  many  pages  did  she 
read  in  all  ? 

4.  A  traveler  paid  9  shillings   a  day  for 
his  board,  and  7  shillings  a  day  for  his  horse; 
how  much  did  he  pay  for  both  1 

5.  Annie  had  9  pictures,  and  her  brother 
gave  her  2  more ;  how  many  had  she  then  ? 

6.  If  a  peck  of  apples  cost  9  cents,  and  a 
head  of  cabbage  4  cents,  what  will  both  cost  ? 

7.  In  a  certain  class  there  are  9  boys  and 
8  girls;  ho/v-  many  scholars  are  there  in  the 
class  I 

8.  There  are  9  geese  and  9  ducks  swim- 
ming in  a  pond ;  how  many  of  both  I 


20  ADDITION. 


LESSON   XI 


10  and  1  are  11 

10  and  2  are  12 

10  and  3  are  13 

10  and  4  are  14 

10  and  5  are  15 


10  and  6  are  16 

10  and  7  are  17 

10  and  8  are  18 

10  and  9  are  19 

10  and  10  are  20 


1.  If  a  man  give  10  dollars  for  a  harness, 
and  4  dollars  for  a  whip,  how  much  does  he 
give  for  both  ? 

2.  A  farmer  has  10  sheep  in  one  lot,  and 

9  in  another  ;    how  many  has  he  in  both  ] 

3.  A  tailor  sold  a  coat  for  10  dollars,  and 
a  pair  of  pantaloons  for  6  dollars;  how  much 
did  he  receive  for  both  ? 

4.  A  beggar  met  two  boys ;  one  gave  him 

10  cents,  and  the  other  7  cents ;  how  many 
cents  did  they  both  give  him  ? 

5.  There  were  8  boys  on  one  bench,  and 
10  on  another;    how  many  boys  on  both 
benches  ? 

6.  Alice  had   10  cents,  and  her  mother 
gave  her  2  more ;  how  many  had  she  then  ? 

7.  Bought  a  pig  for  3  dollars,  and  a  calf 
for  10  dollars ;  how  much  did  I  pay  for  both  ? 

8.  Charles  picked  10  pears  from  a  tree, 
and  left  10  on  it;  how  many  were  on  the 
tree  at  first  ? 


ADDITION. 

21 

LESSON 

X 

I 

I. 

PROMISCUOUS    REVIEW. 

2 

and 

5 

are 

how 

many? 

7 

and 

9 

are 

how 

many  ? 

6 

and 

2 

are 

how 

many  ? 

6 

and 

5 

are 

how 

many  ? 

2 

and 

4 

are 

how 

many? 

3 

and 

6 

are 

how 

many? 

8 

and 

9 

are 

how 

many? 

4 

and 

4 

are 

how 

many  ? 

9 

and 

4 

are 

how 

many? 

7 

and 

8 

are 

how 

many  ? 

4 

and 

7 

arc 

how 

many? 

9 

and 

3 

are 

how 

many  ? 

8 

and 

6 

are 

how 

many? 

2 

and 

9 

are 

how 

many? 

6 

and 

3 

are 

how 

many? 

5 

and 

4 

are 

how 

many? 

7 

and 

2 

are 

how 

many  ? 

3 

and 

8 

are 

how 

many? 

3 

and 

3 

are 

how 

many? 

5 

and 

6 

are 

how 

many? 

3 

and 

9 

are 

how 

many? 

5 

and 

8 

are 

how 

many? 

4 

and 

5 

are 

how 

many? 

4 

and 

2 

are 

how 

many? 

9 

and 

8 

are 

how 

many? 

3 

and 

7 

are 

how 

many? 

8 

and 

5 

are 

how 

many? 

6 

and 

4 

are 

how 

many? 

4 

and 

9 

are 

how 

many? 

7 

and 

6 

are 

how 

many  ? 

5 

and 

4 

are 

how 

many  ? 

6 

and 

8 

are 

how 

many? 

2 

and 

7 

are 

how 

many? 

9 

and 

5 

are 

how 

many? 

7 

and 

5 

are 

how 

many? 

8 

and 

3 

are 

how 

many? 

2 

and 

3 

are 

how 

many? 

9 

and 

6 

are 

how 

many? 

5 

and 

2 

are 

how 

many? 

5 

and 

7 

are 

how 

many? 

6 

and 

9 

are 

how 

many? 

4 

and 

G 

are 

how 

many? 

7 

and 

7 

are 

how 

many? 

7 

and 

3 

are 

how 

many  ? 

3 

and 

4 

are 

how 

many  ? 

2 

and 

8 

are 

how 

many  ? 

8 

and 

7 

are 

how 

many? 

5 

and 

9 

are 

how 

many  ? 

4 

and 

8 

are 

how 

many? 

8 

and 

8 

are 

how 

many  ? 

9 

and 

2 

are 

how 

many? 

6 

and 

7 

are 

how 

many? 

5 

and 

3 

are 

how 

many  ? 

5 

and 

5 

are 

how 

many  ? 

6 

and 

G 

are 

how 

many  ? 

9 

and 

7 

are 

how 

many  ? 

3 

and 

5 

are 

how 

many? 

2 

and 

G 

are 

how 

many? 

7 

and 

4 

are 

how 

many  ? 

9 

and 

9 

are 

how 

many? 

22  ADDITION. 


LESSON    XIII. 

PROMISCUOUS    EXAMPLES. 

1.  Henry  paid  6  cents  for  an  inkstand,  4 
cents  for  some  pens,  and  5  cents  for  a  writing 
book ;  how  much  did  he  pay  for  all  I 

ANALYSIS.  —  He  paid  as  many  cents  as  the  sum  of  6 
cents,  4  cents,  and  5  cents  ;  6  cents  and  4  cents  are  10 
cents ,  and  5  cents  are  15  cents.  Therefore,  fyc. 

2.  A  drover  bought  4  cows  of  one  man,  3 
of  another,  and  7  of  another ;  how  many  cows 
did  he  buy  in  all  I 

3.  Elizabeth  gave  10  cents  for  three  spools 
of  thread,  b  cents  for  a  thimble,  and  9  cents 
for  some  needles ;  how  many  cents  did  she 
give  for  all  ] 

4.  A  lady  bought  a  dress  for  8  dollars,  a 
shawl  for  9  dollars,  and  a  parasol  for  2  dollars ; 
how  many  dollars  did  she  pay  for  them  all  ? 

5.  If  a  man  paid  6  dollars  for  a  cord  of 
wood,  5  dollars  for  a  ton  of  hay,  7  dollars 
for  some  pork,  and  3  dollars  for  some  beef, 
how  many  dollars  did  he  pay  for  the  whole  ? 

6.  A  boy  traveled  6  miles  one  day,  8  miles 
the  next  day,  and  10  miles  the  next ;  how 
many  miles  did  he  travel  in  three  days  ? 

7.  A  cabinet  maker  asked  12  dollars  for  a 
bureau,  10  dollars  for  a  table,  and  5  dollars 
for  a  stand ;  what  was  his  price  for  the  whole  ? 


SUBTEACTION. 


23 


LESSON    I. 

Taking  a  less  number  or  quantity  from  a  greater,  is 
called  SUBTRACTION. 


leaves    flSjL. 
rabbits,  rabbit. 

1  3  2 

2.  H  taken  from  (||)  ||||  leaves  ||J| 
hat  hats,  hats. 

2  42 

3.  f^>  Q  taken  from  00 (GO)  leaves  06 

eggs- 


2 


tulips 
3 


glasses 
3 


birds 


taken  from 


taken  from 


taken  from  * 


leaves  I 


tulips. 


h  CJESjif^Si 

I  rH  <nt|  leaves  how 
glasses, 


tulips, 
5 


4 

birds, 


leaves  how 
many? 


24  SUBTRACTION. 


LESSON    II, 


1  from  1  leaves  0 
1  from  2  leaves  1 
1  from  3  leaves  2 
1  from  4  leaves  3 
1  from  5  leaves  4 


1  from  6  leaves  5 
1  from  7  leaves  6 
1  from  8  leaves  7 
1  from  9  leaves  8 
1  from  10  leaves  9 


1.  A  boy,  having  3  apples,  gave  1  to  his 
sister ;  how  many  had  he  left  ? 

ANALYSIS.  —  He  had  as  many  apples  left  as  the  dif- 
ference between  3  apples  and  1  apple,  which  is  2  apples. 
Therefore,  since  a  boy  had  3  apples,  and  gave  1  apple  to 
his  sister,  he  had  2  apples  left. 

2.  A  poor  woman  who  had  6  cents,  lost  1 ; 
how  many  had  she  left  I 

3.  A  tailor  had  7  yards  of  cloth ;  he  cut 
off  1  yard  ;  how  many  yards  had  he  left  1 

4.  Mary  had  8   credit  marks,  and  1  de- 
merit  mark ;  how  many  more  credit  than 
demerit  marks  had  she  ? 

5.  Robert  found  5  ripe  pears  under  a  tree, 
and  ate  1  of  them  ;  how  many  had  he  left  ? 

6.  If  you  make  10  marks  on  your  slate, 
and  rub  out  1,  how  many  remain  ? 

7.  If   I   pay   4   dollars   for  a   barrel   of 
flour,  and  1  dollar  for  a  bushel  of  corn,  how 
much  more  do  I  pay  for  the  flour  than  for 
the  corn  ? 


SUBTRACTION.  25 


LESSON    III. 


2  from  2  leaves  0 
2  from  3  leaves  1 
2  from  4  leaves  2 
2  from  5  leaves  3 
2  from  6  leaves  4 


2  from  7  leaves  5 
2  from  8  leaves  6 
2  from  9  leaves  7 
2  from  10  leaves  8 
2  from  11  leaves  9 


1.  Alice  had  4  peaches,  and  gave  2  to 
Rollin  ;  how  many  had  she  left  ? 

ANALYSIS.  —  She  had  as  many  peaches  left  as  the  dif- 
ference between  4  peaches  and  2  peaches,  which  is  2 
peaches.  Therefore,  since  Alice  had  4  peaches,  and  gave 
2  to  Rollin,  she  had  2  peaches  left. 

2.  Lucy  had  6  sheets  of  paper,  and  gave  2 
to  Ann ;  how  many  had  she  left  ] 

3.  There  were  8  pigeons  on  a  tree,  and  2 
flew  away ;  how  many  were  there  left  I 

4.  Frank  had  2  apples  when  he  started 
for  school ;  he  gave  2  away  ;  how  many  had 
he  left  ? 

5.  Ella  had  5  roses,  and  gave  2  to  her 
teacher ;  how  many  had  she  left  ? 

6.  Clinton   had    7    chickens,    and    a   cat 
caught  2  of  them  ;  how  many  had  he  left  I 

7.  A  tinner  had  3  milk  pails,  and  sold  2 
of  them  ;  how  many  had  he  left  ? 

8.  Willie  had  9  cents,  and  gave  2  cents 
to  a  blind  man  ;  how  many  had  he  left  I 


26  SUBTRACTION. 


LESSON    IV. 


3  from  3  leaves  0 
3  from  4  leaves  1 
3  from  5  leaves  2 
3  from  6  leaves  3 
3  from  7  leaves  4 


3  from  8  leaves  5 
3  from  9  leaves  6 
3  from  10  leaves  7 
3  from  1 1  leaves  8 
3  from  12  leaves  9 


1.  Mr.  Jones  sold  some  hay  for  7  dollars, 
and  received  3  dollars ;  how  much  more  was 
due  ? 

ANALYSIS.  —  As  much  more  was  due  as  the  difference 
between  7  dollars  and  3  dollars,  which  is  4  dollars. 
Therefore9  since  Mr.  Jones  sold  some  hay  for  7  dollars^ 
and  received  3  dollars,  there  were  four  dollars  more  due. 

2.  Samuel  found  5  eggs,  and  broke  3  of 
them ;  how  many  had  he  left? 

3.  Marcus  borrowed  10  cents,  and  paid  3 ; 
how  much  did  he  then  owe  ? 

4.  A  merchant  bought  9  barrels  of  flour, 
and  sold  all  but  3  barrels ;  how  many  did  he 
sell? 

5.  A  man  had  12  sheep  in  a  pasture,  and 
3  of  them  jumped  out ;  how  many  remained  ? 

6.  Daniel  had  3  apples,  and  gave  each  of 
his  three  sisters  one  apiece ;   how  many  had 
he  left  ? 

7.  A  farmer  had  6  horses,  and  sold  all  but 
3 ;  how  many  did  he  sell  1 


SUBTRACTION.  27 


LESSON   V, 


4  from  4  leaves  0 
4  from  5  leaves  1 
4  from  6  leaves  2 
4  from  7  leaves  3 
4  from  8  leaves  4 


4  from  9  leaves  5 
4  from  10  leaves  6 
4  from  11  leaves  7 
4  from  12  leaves  8 
4  from  13  leaves  9 


1.  A   farmer,  having   8   pigs,  sold  4  of 
them  ;  how  many  had  he  left  ? 

ANALYSIS.  —  He  had  as  many  pigs  left  as  the  differ- 
ence between  8  pigs  and  4  pigs,  which  is  4  pigs.  There- 
fore, since  a  farmer  had  8  pigs,  and  sold  4  of  them,  he 
had  4  pigs  left. 

2.  A  boy  caught  10  fishes,  and  threw  4 
of  them  back  into  the  creek ;  how  many  had 
he  left  ? 

3.  Bought  a  saddle  for  13  dollars,  and  a 
bridle  for  4  dollars ;  how  much  more  did  I 
pay  for  the  saddle  than  for  the  bridle  I 

4.  There  were  9  passengers  in  the  stage,  4 
of  whom  got  out;   how  many  remained  in 
the  stage  ] 

5.  Laura  found  11  roses  on  her  bush;  and 
picked  4 ;  how  many  remained  on  the  bush  I 

6.  A  man  paid  6  shillings  for  his  dinner, 
and  4  shillings  for  his  breakfast;  how  much 
more  did  he  pay  for  his  dinner  than  for  his 
breakfast  ? 


28  SUBTRACTION. 


LESSON    VI. 


5  from  5  leaves  0 
5  from  6  leaves  1 
5  from  7  leaves  2 
5  from  8  leaves  3 
5  from  9  leaves  4 


5  from  10  leaves  5 
5  from  11  leaves  6 
5  from  12  leaves  7 
5  from  13  leaves  8 
5  from  14  leaves  9 


1.  A  man  earned  7  dollars  in  a  week,  and 
spent  5  dollars  of  it ;  how  many  did  he  save  I 

2.  If  10  gallons  of  water  run  into  a  cistern 
in  a  minute,  and  5  gallons  run  out,  how 
many  remain  ? 

3.  A  peddler  had  8  penknives,  and  sold  5 
of  them ;  how  many  had  he  left  ? 

4.  Alfred  fired  into  a  flock  of  12  wild 
pigeons,  and  killed  5  of  them;  how  many 
flew  away? 

5.  A  woman  bought  14  yards  of  calico, 
and  used  5  yards ;  how  many  yards  had  she 
left? 

6.  Carlos,  having  11  cents,  gave  5  of  them 
for  an  orange ;  how  many  had  he  left  I 

7.  Stephen  caught  13  fish,  and  gave  5  of 
them  to  a  poor  woman ;  how  many  had  he 
left? 

8.  On  a  rose  bush  are  6  white  roses,  and  I 
Eliza  picks  5  of  them  for  the  flower  vase ;  j 
how  many  are  left  on  the  bush  I 


SUBTRACTION.  29 


LESSON   VII. 


6  from  6  leaves  0 
6  from  7  leaves  1 
6  from  8  leaves  2 
6  from  9  leaves  3 
6  from  10  leaves  4 


6  from  11  leaves  5 
6  from  12  leaves  6 
6  from  13  leaves  7 
6  from  14  leaves  8 
6  from  15  leaves  9 


1.  A  boy  gave  14  cents  for  a  knife,  and 
sold  it  for  6  cents ;  how  much  did  he  lose  1 

2.  In  a  spelling  class  are  7  girls  and  6 
boys ;  how  many  more  girls  than  boys  in  the 
class  ] 

3.  A  merchant  bought  9  barrels  of  salt, 
and  after  selling   some,  he  found   he   had 
6  barrels   left;    how  many  barrels  did  he 
sell! 

4.  If  I  owe  15  dollars,  and  pay  6  dollars, 
how  much  do  I  still  owe  ? 

5.  Stephen  had  13  marbles,  and  lost  6  of 
them  ;  how  many  had  he  left  ? 

6.  There  are  12  sheep  in  a  yard,  and  a 
dog  bites  all  but  6  of  them;  how  many  does 
he  bite  1 

1.  Arthur  rode  11  miles  in  the  cars,  and  6 
in  the  stage ;  how  many  more  miles  did  he 
ride  in  the  cars  than  in  the  stage  I 

8.  Carrie  has  6  roses,  and  gives  6  to  her 
teacher ;  how  many  has  she  left  \ 

3~* 


30  SUBTRACTION. 


LESSON   VIII. 


7  from  7  leaves  0 
7  from  8  leaves  1 
7  from  9  leaves  2 
7  from  10  leaves  3 
7  from  11  leaves  4 


7  from  12  leaves  5 
7  from  13  leaves  6 
7  from  14  leaves  7 
7  from  15  leaves  8 
7  from  16  leaves  9 


1.  Edgar   had    12    chickens,    and   a   cat 
killed  7  of  them ;  how  many  chickens  had 
he  left] 

2.  Julius  had  7  cents,  and  his  father  gave 
him  enough  more  to  make  15 ;  how  many 
cents  did  his  father  give  him  ? 

3.  A  young   lady   went    shopping   with 
16    dollars ;    when    she    returned    she   had 
only  7   dollars;   how  much  money  did  she 
spend  ? 

4.  During  13  days,  it  rained  7  days;  how 
many  fair  days  were  there  I 

5.  In  a  class  of  11  scholars,  7  recited  per- 
fect lessons ;    how  many  had  imperfect  les- 
sons ? 

6.  In  a  yard  there  were  9  shade  trees,  and 
the  wind  blew  down  7;    how   many  were 
left  standing? 

7.  A  man  bought  a  calf  for  7  dollars,  and 
sold  it  for   10  dollars;   how  much  did  he 
gain  ? 


SUBTRACTION.  81 


LESSON    IX. 


8  from  8  leaves  0 
8  from  9  leaves  1 
8  from  10  leaves  2 
8  from  11  leaves  3 
8  from  12  leaves  4 


8  from  13  leaves  5 
8  from  14  leaves  6 
8  from  15  leaves  7 
8  from  16  leaves  8 
8  from  17  leaves  9 


1.  A  farmer,  having  15  sheep,  sold  8  of 
them ;  how  many  had  he  left  1 

2.  Thornton  had  9  merit  marks,  and  8 
[  demerit  marks ;  how  many  more  merit  than 

demerit  marks  had  he  ? 

3.  Peter  carried  10  quarts  of  herries  to 
market,  and  sold  8  quarts ;  how  many  quarts 
had  he  left  1 

4.  A  man  sold  a  cow  for  17  dollars,  and 
took  a  plow  worth  8  dollars,  and  the  bal- 
ance in  money;   how  much  money  did  he 
receive  ? 

5.  There  were  14  yards  in  a  piece  of  me- 
rino, and  a  lady  bought  8  yards  for  a  dress ; 
how  many  yards  were  left  ^ 

6.  In  a  row  of  12  shade  trees,  8  of  them 
die ;  how  many  are  left  ] 

7.  Calvin,  having  16  cents,  paid  8  cents 
for  a  slate ;  how  many  had  he  left  I 

8.  Emma  is  11  years  old,  and  Willie  8; 
what  is  the  difference  in  their  ages  ^ 


32  SUBTRACTION. 


LESSON    X. 


9  from  9  leaves  0 
9  from  10  leaves  1 
9  from  11  leaves  2 
9  from  12  leaves  3 
9  from  13  leaves  4 


9  from  14  leaves  5 
9  from  15  leaves  6 
9  from  16  leaves  7 
9  from  17  leaves  8 
9  from  18  leaves  9 


1.  James  sold  his  colt  for  16  dollars,  and 
received  in  payment  9  dollars'  worth  of  goods, 
and  the  rest  in  money ;  how  much  money  did 
he  receive  I 

2.  Clorinda  had   10   cents,  and   gave   9 
cents  for  a  new  slate ;  how  many  cents  had 
she  left? 

3.  A  painter  bought  1 1  gallons  of  oil,  and 
after  using  9  gallons,  sold  the  remainder; 
how  much  did  he  sell  ? 

4.  A  grocer  bought  a  quantity  of  butter 
for  12  dollars,  and  it  being  damaged,  he  was 
obliged  to  sell  it  for  9  dollars ;  how  much 
did  he  lose  by  the  bargain  ? 

5.  Austin,  having  15  steel  pens,  gave  away 
all  but  9  of  them;  how  many  did  he  give 
away  ? 

6.  A  man  borrowed  14  dollars,  and  paid  9 
of  it ;  how  much  did  he  still  owe  ? 

7.  A  farmer   had   9    sheep,  and   bought 
enough  to  make  18 ;  how  many  did  he  buy? 


SUBTRACTION.  83 


LESSON   XI. 


10  from  10  leaves  0 
10  from  11  leaves  1 
10  from  12  leaves  2 
10  from  13  leaves  3 
10  from  14  leaves  4 


10  from  15  leaves  5 
10  from  16  leaves  6 
10  from  17  leaves  7 
10  from  18  leaves  8 
10  from  19  leaves  9 


1.  Ralph  earned  17  cents  and  received  10 
cents ;  how  much  is  still  due  him  I 

2.  In  a  certain  school  are  18  girls  and  10 
boys ;  how  many  more  girls  than  boys  are 
there  ? 

3.  A  grocer  had  12  boxes  of  lemons,  and 
sold    10  boxes;    how  many  boxes  had  he 
left? 

4.  In  a  school  there  are  10  boys  and  16 
girls ;  how  many  more  girls  than  boys  I 

5.  Ella  had  14  roses,  and  gave  away  10  of 
them  ;  how  many  had  she  left  ? 

6.  A  man  bought  a  keg  of  molasses  con- 
taining 15  gallons;  having  used  a  part  of  it, 
he  found  there  were  10  gallons  left ;   how 
many  gallons  did  he  use  I 

7.  Edgar  had  19  cents,  and  spent  10  of 
them  ;  how  many  cents  had  he  left  1 

8.  A  farmer  had  13  acres  of  wheat,  and 
10  acres  of  corn;  how  many  acres  more  of 
wheat  had  he  than  of  corn  ? 


34                                     SUBTRACTION. 

LESSO 

PROMISCUOl 

5  from  14  how  many? 
2  from     8  how  many  ? 
5  from     9  how  many? 
9  from  10  how  many? 
6  from     7  how  many  ? 
7  from  12  how  many? 
9  from  12  how  many? 
4  from     8  how  many  ? 
5  from  10  how  many  ? 
6  from  1  1  how  many  ? 

N    XII. 

IS    REVIEW. 

G  from  14  how  many? 
4  from     7  how  many  ? 
8  from  15  how  many? 
5  from  11  how  many? 
7  from  10  how  many? 
3  from     8  how  many? 
3  from  13  how  many? 
9  from  11   how  many? 
6  from  12  how  many? 
8  from  10  how  many? 

8  from     9  how  many? 
7  from  16  how  many  ? 
6  from     9  how  many? 
2  from  11  how  many? 
3  from     7  how  many  ? 
5  from     8  how  many? 
9  from  14  how  many? 
9  from  13  how  many? 
7  from     9  how  many? 
2  from  10  how  many? 

4  from  11  how  many? 
3  from  10  how  many? 
5  from  12  how  many? 
7  from  13  how  many  ? 
8  from  12  how  many? 
9  from  16  how  many? 
7  from     8  how  many? 
6  from  13  how  many? 
5  from     7  how  many? 
4  from  12  how  many? 

3  from     9  how  many  ? 
7  from  15  how  many? 
8  from  17  how  many? 
4  from  10  how  many? 
2  from     9  how  many? 
7  from  14  how  many? 
3  from  11  how  many? 
5  from  13  how  many? 
9  from  17  how  many? 
8  from  14  how  many? 

8  from  16  how  many? 
9  from  15  how  many? 
7  from  11   how  many? 
4  from     9  how  many? 
3  from   12  how  many? 
6  from  15  how  many? 
9  from  18  how  many? 
8  from  1  1   how  many  ? 
6  from  10  how  many  ? 
4  from  13  how  many  ? 

SUBTRACTION.  85 


LESSON    XIII. 

PROMISCUOUS   EXAMPLES. 

1.  Oscar  had  16  cents;  he  gave  6  cents 
to  a  beggar,  and  5  cents  for  an  orange ;  how 
many  had  he  left  ? 

ANALYSIS.  —  He  had  left  the  difference  between  16 
cents,  and  the  sum  of  6  cents  and  5  cents  ;  6  cents  and  5 
cents  are  11  cents,  and  11  cents  from  16  cents  leaves  5 
cents.  T/ierefore,  fyc. 

2.  A  farmer,  having  18  sheep,  sold  7  at 
one  time,  and  4  at  another ;   how  many  had 
he  left  1 

3.  A  grocer  bought  10  dozen  of  eggs  of 
one  man  and  9  dozen  of  another ;  he  then 
sold  6  dozen  to  one  of  his  neighbors,  and 
kept  the  rest  for  his  own  use ;  how  many 
did  he  keep  ] 

4.  A  farmer  bought  a  cow  for  15  dollars ; 
he  paid  one  10  dollar  bill,  and  one  3  dollar 
bill ;  how  much  did  he  still  owe  ? 

5.  A  boy,  having  17  chickens,  sold  5  of 
them  at  one  time,  7  at  another,  and  2  at  an- 
other ;  how  many  had  he  left  ? 

6.  Sold  some  pork  for  12  dollars,  and 
received  some  sugar  worth  3  dollars,  a  hat 
worth  2  dollars,  some  cloth  worth  4  dollars, 
and  the  rest  in  money;  how  much  money 
did  I  receive  ? 


36 


MULTIPLICATION. 


LESSON   I. 

MULTIPLICATION  is  taking  one  number  as  many  times 
as  there  are  units  in  another :  thus, 

1.  If  2  boys  have  2  apples  apiece,  how  many  apples 
will  both  have  ? 


Two  times  two  are  how  many  ? 

2.  If  there  are  3  combs  in  one  box,  how  many  combs 
would  there  be  in  2  boxes  ? 


Two  times  three  are  how  many  ? 

3.  If  3  men  have  2  dogs  each,  how  many  dogs  will 
they  all  have  ? 


Three  times  two  are  how  many  ? 

4.  If  1  man'  can  make  2  boots  in  three  days,  how 
many  boots  can  4  men  make  ? 

<JJ><*lHtJL<Jt> 

Two  times  four  are  how  many  ? 

5.  If  there  are  3  owls  in  each  of  3  cages,  how  many 
owls  in  all  ? 


Three  times  three  are  how  many  ? 


MULTIPLICATION.  37 


LESSON     II. 


once  1  is  1 

once  2  is  2 

once  3  is  3 

once  4  is  4 

once  5  is  5 


once  6  is  6 

once  7  is  7 

once  8  is  8 

once  9  is  9 

once  10  is  10 


1.  At  1  cent  each,  what  will  2  eggs  cost  ? 

ANALYSIS.  —  Since  1  egg  cost  1  cent,  2  eggs,  which 
are  2  times  1  egg,  will  cost  2  times  1  cent,  which  are  2 
cents.  Therefore,  at  1  cent  each,  2  eggs  will  cost  2 
cents. 

2.  If  a  man  earn  1  dollar  a  day,  how  much 
can  he  earn  in  4  days  ^ 

3.  If  Rollin  reads  1  hour  each  evening, 
how  many  hours  will  he   read  in   6  even- 
ings ] 

4.  What  will  5  bushels  of  wheat  cost,  at 
1  dollar  a  bushel  ? 

5.  At  1  cent  each,  what  will  9  steel  pens 
costl 

6.  If  a  family  eat  1  bushel  of  corn  in  a 
week,  how  many  bushels  would  they  eat  in 
10  weeks  ? 

7.  If  Thomas  gets  1  credit  mark  a  day, 
how  many  credit  marks  will  he  get  in  7  days  ? 

8.  If  Henry  write    1    page  a  day,   how 
many  pages  will  he  write  in  8  days  I 


38  MULTIPLICATION. 


LESSON     III, 


2  times  1  are  2 
2  times  2  are  4 
2  times  3  are  6 
2  times  4  are  8 
2  times  5  are  10 


2  times  6  are  12 
2  times  7  are  14 
2  times  8  are  16 
2  times  9  are  18 
2  times  10  are  20 


1.  What  will  2  pounds  of  rice  cost,  at  6 
cents  a  pound  I 

ANALYSIS. —  Since  1  pound  costs  6  cents,  2  pounds, 
which  are  2  times  1  pound,  will  cost  2  ta'?ftes  6  cew&, 
which  are  12  m^s.  T/ierefore  2  pounds  of  rice  will 
cost  12  cerate,  a£  6  cents  a  pound. 

2.  Sarah  gave   2   girls   3  apples  apiece; 
how  many  did  she  give  them  both  ? 

3.  If  on  one  rose  bush  there  are  4  roses, 
how  many  on  2  bushes  1 

4.  Almira  bought  2  yards  of  ribbon  at  5 
cents  a  yard ;  how  much  did  she  pay  for  the 
whole  ? 

5.  At  7  cents  a  pound,  what  will  2  pounds 
of  sugar  cost  ? 

6.  What  will  2  tons  of  hay  cost,  at  9  dol- 
lars a  ton  ? 

7.  At  5  shillings  a  bushel,  what  will  be 
the  cost  of  2  bushels  of  corn  ? 

8.  At  2  cents  apiece,  what  will  2  pears 
cost] 


MULTIPLICATION.  39 


LESSON    IV. 


3  times  1  are  3 
3  times  2  are  6 
3  times  3  are  9 
3  times  4  are  12 
3  times  5  are  15 


3  times  6  are  18 
3  times  7  are  21 
3  times  8  are  24 
3  times  9  are  27 
3  times  10  are  30 


1.  If  a  man  earn  9  dollars  in  one  week, 
how  many  dollars  will  he  earn  in  3  weeks  1 

ANALYSIS.  —  If  a  mant  earn  9  dollars  in  1  week,  in 
3  weeks,  which  are  3  times  1  week,  he  will  earn  3  times 
9  dollars,  which  are  27  dollars.  Therefore,  if  a  man 
earn  9  dollars  in  1  week,  he  will  earn  27  dollars  in  3 


2.  If  a  farmer  give  4  bushels  of  corn  for 
one  yard  of  cloth,  how  many  bushels  must 
he  give  for  3  yards  ? 

3.  At  8  shillings  a  yard,  what  will  3  yards 
of  silk  cost  ? 

4.  In  one  cent  are  10  mills;  how  many 
mills  in  3  cents'? 

5.  When  sugar  is  worth  7  cents  a  pound, 
what  will  3  pounds  cost  1 

6.  A   drover  paid    3    dollars   a  head   for 
sheep ;  how  much  did  he  pay  for  3  sheep  1 

7.  Egbert  gave  three  of  his  classmates  5 
apples  apiece  ;  how  many  apples  did  he  give 
them  all  ? 


40  MULTIPLICATION. 


LESSON    V. 


4  times  1  are  4 
4  times  2  are  8 
4  times  3  are  12 
4  times  4  are  16 
4  times  5  are  20 


4  times  6  are  24 
4  times  7  are  28 
4  times  8  are  32 
4  times  9  are  36 
4  times  10  are  40 


1.  What  will  4  yards  of  ribbon  cost,  at  4 
cents  a  yard  ? 

ANALYSIS.  —  Since  1  yard  of  ribbon  costs  4  cents, 
4  yards,  which  are  4  times  1  yard,  will  cost  4  ft'mes  4 
ce/zte,  wfo'cA  are  1 6  cents.  Therefore,  4  yards  of  ribbon, 
at  4  ceftte  a  yara7,  mY/  eos£  1 6  cents. 

2.  If  a  horse  eat  8  quarts  of  oats  a  day, 
how  many  quarts  will  he  eat  in  4  days  ? 

3.  At  9  shillings  a  day,  what  will  4  days' 
work  come  to  ] 

4.  If  one  bench  will  seat  6  pupils,  how 
many  pupils  will  4  benches  seat  ] 

5.  Martha's  dress  contains  7  yards  of  mus- 
lin, at  4  shillings  a  yard ;  what  was  the  cost 
of  the  dress  ? 

6.  If  Joseph  walk  3  miles  in  an  hour, 
how  far  will  he  walk  in  4  hours  ] 

7.  A  butcher  bought  4  calves  at  5  dollars 
apiece  ;  what  did  they  cost  1 

8.  At  2  shillings   a  quart,  what  will  4 
quarts  of  molasses  cost  I 


MULTIPLICATION.  41 


LESSON   VI. 


5  times  1  are  5 
5  times  2  are  10 
5  times  3  are  15 
5  times  4  are  20 
5  times  5  are  25 


5  times  6  are  30 
5  times  7  are  35 
5  times  8  are  40 
5  times  9  are  45 
5  times  10  are  50 


1.  There  are  7  days  in  1  week ;  how  many 
days  in  5  weeks  1 

2.  How  far  will  a  boat  sail  in  5  hours,  at 
at  the  rate  of  9  miles  an  hour  ? 

3.  What  will  5  barrels  of  flour  cost,  at  5 
dollars  a  barrel  1 

4.  How  many  yards  are  there  in  5  pieces 
of  cloth,  if  there  are  10  yards  in  each  piece  ? 

5.  If  an  orange  is  worth  4  apples,  how 
many  apples  are  5  oranges  worth  1 

6.  If  a  pupil  work  6  problems  a  day,  how 
many  problems  will  he  work  in  5  days  ? 

7.  Carlos  gave  5  beggars  5  cents  apiece ; 
how  many  cents  did  he  give  them  all  I 

8.  If  a  horse  travel  8  miles  an  hour,  how 
far  can  he  travel  in  5  hours  I 

9.  Which  is  greater,  5  times  8,  or  4  times 
10? 

10.  Which  is   greater,   4  times   6,   or  3 
times  815  times  6,  or  3  times  101,5  times 
8,  or  4  times  9  1 


42  MULTIPLICATION. 


LESSON   VII. 


6  times  1  are  6 
6  times  2  are  12 
6  times  3  are  18 
6  times  4  are  24 
6  times  5  are  30 


6  times  6  are  36 
6  times  7  are  42 
6  times  8  are  48 
6  times  9  are  54 
6  times  10  are  60 


1.  A  farmer  bought  a  plow  for  5  dollars  ; 
what  would  6  plows  cost  at  the  same  rate  ? 

2.  At  2  dollars  a  day,  how  many  dollars 
would  a  man  earn  in  6  days  ? 

3.  What  cost  6  tons  of  hay,  at  7  dollars 
a  ton! 

4.  George  bought  6  lemons  at  4  cents 
apiece ;  what  did  they  all  cost  I 

5.  There  are  8   quarts  in  1  peck;    how 
many  quarts  in  6  pecks  I 

6.  What  will  6  pounds  of  honey  cost,  at 
10  cents  a  pound] 

7.  What  will  6  pounds  of  ginger  cost  at  6 
cents  a  pound] 

8.  In  a  garden  are  6  apple  trees,  and  4 
bushels  of  apples  on  each  tree ;  how  many 
bushels  on  all  the  trees  ? 

9.  Which  is    greater,  6    times    1,    or   0 
times  61 

10.  Which   is   greater,  6    times  5,  or  3 
times   10  I 


MULTIPLICATION.  43 


LESSON   VIII. 


7  times  1  are  7 
7  times  2  are  14 
7  times  3  are  21 
7  times  4  are  28 
7  times  5  are  35 


7  times  6  are  42 
7  times  7  are  49 
7  times  8  are  56 
7  times  9  are  63 
7  times  10  are  70 


1.  If  a  mill  grind  5  bushels  of  wheat  an 
hour,  how  many  bushels  will  it  grind  in  7 
hours  ? 

2.  When  wheat  is  worth  2  dollars  a  bushel, 
what  will  7  bushels  cost  ? 

3.  In  New  England,  6  shillings  make  a 
dollar ;  how  many  shillings  in  7  dollars  ? 

4.  If  you  write  8  lines  in  a  day,  how  many 
lines  will  you  write  in  7  days  ? 

5.  At  10  dollars  a  month,  how  many  dol- 
lars will  a  man  earn  in  7  months  ] 

6.  What  will  be  the  cost  of  7  barrels  of 
flour,  at  7  dollars  a  barrel  ] 

7.  What  are  7  quarts  of  cherries  worth, 
at  4  cents  a  quart  I 

8.  At  9  shillings  a  bushel,  what  will  7 
bushels  of  peaches  cost  ? 

9.  If  there  are  3  sheets  of  paper  in  one 
writing  book,  how  many  sheets  in  7  books  ? 

10.  Which  is    greater,  7    times  6,  or   6 
times  7  I 


44  MULTIPLICATION. 


LESSON    IX, 


8  times  1  are  8 
8  times  2  are  16 
8  times  3  are  24 
8  times  4  are  32 
8  times  5  are  40 


8  times  6  are  48 
8  times  7  are  56 
8  times  8  are  64 
8  times  9  are  72 
8  times  10  are  80 


1.  If  a  ton  of  hay  cost  7  dollars,  what 
will  8  tons  cost  ? 

2.  In  New  York,  8  shillings  make  a  dol- 
lar ;   how  many  shillings  in  5  dollars  ? 

3.  When  coffee  is  worth  10  cents  a  pound, 
what  will  be  the  cost  of  8  pounds  I 

4.  At  4  cents  a  pound,  what  will  8  pounds 
of  rice  cost  ? 

5.  What  will  8  hats  cost,  at  3  dollars 
apiece  ? 

6.  In  one  square  yard  are  9  square  feet ; 
how  many  square  feet  in  8  square  yards  ? 

7.  What  will  8  bushels  of  potatoes  cost, 
at  6  dimes  a  bushel  ? 

8.  At  6  dollars  a  barrel,  what  will  8  bar- 
rels of  flour  cost  ? 

9.  What  is  the  difference  between  8  times 
7,  and  7  times  8  ? 

10.  At   8    cents   a   pound,  what  will   8 
pounds  of  soda  cost  ? 

11.  What  cost  2  slates,  at  8  cents  apiece? 


MULTIPLICATION.  45 


LESSON    X. 


9  times  1  are  9 
9  times  2  are  18 
9  times  3  are  27 
9  times  4  are  36 
9  times  5  are  45 


9  times  6  are  54 
9  times  7  are  63 
9  times  8  are  72 
9  times  9  are  81 
9  times  10  are  90 


1.  If  a  man  travel  by  stage  5  miles  an 
hour,  how  far  will  he  travel  in  9  hours  I 

2.  What  cost  9   lambs,  at  6  shillings  a 
head  ? 

3.  What  will  9  pounds  of  sugar  cost,  at  9 
cents  a  pound  ? 

4.  If  Maria    write    4  lines  a  day,  how 
many  lines  will  she  write  in  9  days  ? 

5.  There  are  10  dollars  in  one  eagle;  how 
many  dollars  in  4  eagles  I 

6.  At  3  cents  a  skein,  wrhat  will  be  the 
cost  of  9  skeins  of  silk  ? 

7.  If  a  man  consume  8  pounds  of  meat  in  | 
a  week,  how  much  will  he  consume    in  9 
weeks  ] 

8.  If  it  take  7  yards  of  calico  to  make  one 
dress,  how  many  yards  will  it  take  to  make 
9  dresses  ] 

9.  What  cost  9  hats  at  3  dollars  apiece  ? 

10.  What  cost  9  pounds  of  nails,  at  6 
cents  a  pound  ? 


46  MULTIPLICATION. 


LESSON    XI. 


10  times  1  are  10 
10  times  2  are  20 
10  times  3  are  30 
10  times  4  are  40 
10  times  5  are  50 


10  times  6  are  60 
10  times  7  are  70 
10  times  8  are  80 
10  times  9  are  90 
10  times  10  are  100 


1.  If  a  barrel  of  apples  is  worth  9  shil- 
lings, what  are  10  barrels  worth  ? 

2.  At  5  dollars  a  yard,  what  are  10  yards 
of  broadcloth  worth  ? 

3.  What  will  be  the  cost  of  10  cords  of 
wood,  at  3  dollars  a  cord  ? 

4.  What  will  be  the  cost  of  10  yards  of 
calico,  at  10  cents  a  yard? 

5.  If  a  man  earn  8  shillings  a  day,  how 
much  will  he  earn  in  10  days? 

6.  If  Margaret  earn  7  shillings  a  week, 
how  much  will  she  earn  in  10  weeks  ? 

7.  In  an    orchard  are  10  rows   of  trees, 
and  6  trees  in  each  row;  how  many  trees 
in  the  orchard  ] 

8.  Ellen  paid  4  shillings  a  yard  for   10 
yards  of  delaine  ;  what  did  the  whole  cost  ] 

9.  What  cost  10  bushels  of  potatoes,  at  2 
shillings  a  bushel  ? 

10.  What  cost  10  pounds  of  sugar  at  10 
cents  a  pound  ] 


MULTIPLICATION.                                  47 

LESSC 

PROMISCUO1 

2  times  8  are  how  many? 
3  times  9  are  how  many? 
4  times  8  are  how  many? 
7  times  5  are  how  many? 
9  times  4  are  how  many? 
6  times  3  are  how  many? 
4  times  9  are  how  many? 
3  times  4  are  how  many? 
5  times  9  are  how  many? 
7  times  6  are  how  many? 

>N    XII. 

US    REVIEW. 

2  times  9  are  how  many? 
8  times  2  are  how  many? 
6  times  5  are  how  many? 
4  times  7  are  how  many? 
9  times  3  are  how  many? 
5  times  7  are  how  many? 
5  times  8  are  how  many? 
9  times  5  are  how  many  ? 
6  times  4  are  how  many? 
8  times  3  are  how  many? 

3  times  7  are  how  many? 
8  times  9  are  how  many? 
6  times  8  are  how  many? 
5  times  6  are  how  many? 
7  times  3  are  how  many? 
6  times  6  are  how  many? 
9  times  7  are  how  many? 
3  times  8  are  how  many? 
4  times  6  are  how  many? 
7  times  4  are  how  many? 

5  times  2  are  how  many? 
7  times  7  are  how  many?   ( 
4  times  2  are  how  many? 
9  times  9  are  how  many? 
4  times  3  are  how  many? 
6  times  9  are  how  many  ? 
2  times  6  are  how  many? 
8  times  5  are  how  many? 
4  times  4  are  how  many? 
9  times  8  are  how  many? 

8  times  7  are  how  many? 
5  times  4  are  how  many? 
3  times  5  are  how  many? 
3  times  4  are  how  many? 
2  times  5  are  how  many  ? 
8  times  6  are  how  many? 
7  times  8  are  how  many? 
5  times  3  are  how  many? 
3  times  6  are  how  many? 
8  times  8  are  how  many? 

7  times    0  are  how  many? 
2  times    4  are  how  many  ? 
5  times    9  are  how  many  ? 
9  times    8  are  how  many? 
3  times    3  are  how  many  ? 
2  times    3  are  how  many  ? 
7  times    4  are  how  many? 
0  times    8  are  how  many? 
3  times    6  are  how  many? 
6  times  10  are  how  many  ? 

48  MULTIPLICATION. 

LESSON   XIII. 

PROMISCUOUS    EXAMPLES. 

1.  If  one  ream  of  paper  cost  5  dollars, 
what  will  9  reams  cost  I 

ANALYSIS.  —  If  1  ream  of  paper  cost  5-  dollars,  9 
reams,  which  are  9  times  1  ream,  will  cost  9  times  5  dol- 
lars, which  are  45  dollars.  Therefore,  fyc. 

2.  At  4  dollars  apiece,  what  is  the  value 
of  3  satin  vests  1  of  6  ?  of  8  ]  of  7  ? 

3.  A  man  bought  5  brooms,  at  2  shillings 
apiece,  and  2  gallons  of  molasses  at  4  shil- 
lings a  gallon ;   what  was  the  cost  of  the 
whole  I 

4.  At  9  dollars  a  month,  how  much  will  a 
man  earn  in  4  months  I  in  6  months  I  in  7 
months  1  in  9  months  ? 

5.  Bought  5  cords- of  wood  at  3  dollars  a 
cord,  and  2  tons  of  hay  at  7  dollars  a  ton ; 
which  cost  the  most,  and  how  much  ? 

6.  How  much  is  6  times  9  less  4  ?  8  times 

7  less  6 1  4  times  7  less  8 1  7  times  7  less  9  1 

7.  Which  is  less,  6  times  8,  or  5  times 
914:  times  10,  or  5  times  813  times  9,  or 
5  times  6  ? 

8.  Peter  sold  his  knife  for  30  cents,  and 
received  in  payment  3  quarts  of  chestnuts  at 

8  cents  a  quart,  and  the  remainder  in  money ; 
how  much  money  did  he  receive  ? 


DIVISION. 


49 


LESSON    I. 

DIVISION  is  finding  how  many  times  one  number  or 
quantity  is  contained  in  another  :  thus, 

1.  How  many  churches  will  three  bells  supply,  if  each 
church  has  one  bell  ? 


One  is  contained  in  three  how  many  times  ? 

2.  If  one  man  can  make  2  axes  in  one  day,  how  many 
days  will  it  take  him  to  make  4  axes  ? 


Two  is  contained  in  four  how  many  times  ? 

3.  A  lady  gave  6  dolls  to  some  children,  giving  them 
2  apiece  ;  to  how  many  children  did  she  give  the  dolls  ? 


Two  is  contained  in  six  how  many  times  ? 

4.  If  a  chair-maker  can  make  3  chairs  in  a  day,  how 
many  days  will  it  take  him  to  make  9  chairs  ? 


Three  is  contained  in  nine  how  many  times? 

5.  James  gave  8  bunches  of  grapes  to  his  sisters,  giv- 
ing them  4  bunches  each ;  how  many  sisters  had  he  ? 


Four  is  contained  in  eight  how  many  times  ? 


50 


DIVISION. 


LESSON    II. 

1  in  1,  1  time 

1  in     6,     6  times 

1  in  2,  2  times 

1  in     7,     7  times 

1  in  3,  3  times 

1  in     8,     8  times 

1  in  4,  4  times 

1  in     9,     9  times 

1  in  5,  5  times 

1  in  10,  10  times 

2  in     2,  1  time 

2  in  12,     6  times 

2  in     4,  2  times 

2  in  14,     7  times 

2  in     6,  3  times 

2  in  16,     8  times 

2  in     8,  4  times 

2  in  18,     9  times 

2  in  10,  5  times 

2  in  20,  10  times 

1.  At  2  cents  apiece,  how  many  peaches 
can  be  bought  for  6  cents  ? 

ANALYSIS.  —  Since  2  cents  will  buy  1  peachy  6  cents 
will  buy  as  many  peaches  as  2  cents,  the  price  of  1  peachy 
is  contained  times  in  6  cents,  which  are  3  times.     There- 
fore) at  2  cents  apiece,  3  peaches  can  be  bought  for  6  cents. 

2.  At  2  cents  apiece,  how  many  oranges 
can  you  buy  for  8  cents  ?  for  16  cents  ] 
3.  If  a  man  walk  2  miles  an  hour,  how 

long  will  it  take  him  to  walk  14  miles'? 
4.  At    2   shillings   a  bushel,   how   many 
bushels  of  apples  can  be  bought  for  18  shil- 
lings ] 
5.  At  1  dollar  a  yard,  how  many  yards  of 
cloth  can  be  bought  for  9  dollars  ? 

DIVISION. 


51 


LESSON    III. 

3  in     3,  1  time          3  in  18,  6  times 

3  in     6,  2  times         3  in  21,  7  times 

3  in     9,  3  times         3  in  24,  8  times 

3  in  12,  4  times         3  in  27,  9  times 

3  in  15,  5  times         3  in  30,  10  times 


1.  At  3  dollars  a  cord,  how  many  cords 
of  wood  can  be  bought  for  12  dollars  ? 

ANALYSIS. —  Since  3  dollars  will  buy  1  cord,  12  dol- 
lars will  buy  as  many  cords  as  3  dollars,  the  price  of 
1  cord,  is  contained  times  in  12  dollars,  which  are  4 
times.  Therefore,  at  3  dollars  a  cord,  4  cords  of  wood 
can  be  bought  for  12  dollars. 

2.  For  21  cents,  how  many  yards  of  rib- 
bon can  you  buy,  at  3  cents  a  yard  ? 

3.  If  the  cars  run  a  mile  in  3  minutes, 
how  many  miles  will  they  run  in  30  min- 
utes ] 

4.  A  father  divided  24  marbles  among  his 
3  boys  ;  how  many  did  he  give  to  each  ? 

5.  How  many  lemons,  at  3  cents  apiece, 
can  be  bought  for  18  cents  ] 

6.  At  3  cents  a  quart,  how  many  quarts 
of  milk  can  be  bought  for  27  cents  ] 

7.  Harriet  paid  3  cents  a  spool  for  some 
thread  ;  how  many  spools  could  she  buy  for 
15  cents  I 


52 


DIVISION. 


LESSON    IV. 


4  in    4,  1  time 
4  in    8,  2  times 
4  in  12,  3  times 
4  in  16,  4  times 
4  in  20,  5  times 


4  in  24,  6  times 
4  in  28,  7  times 
4  in  32,  8  times 
4  in  36,  9  times 
4  in  40,  10  times 


1.  If  4  boys  can  sit  on  one  seat,  how  many 
seats  will  accommodate  20  boys  ? 

2.  If  a  class  of  4  boys  answer  28  ques- 
tions, how  many  will  each  answer  ? 

3.  Clinton  earned  40  cents  in  4  days ;  how 
many  cents  did  he  earn  in  one  day  ? 

4.  If  bonnets  are  4  dollars  apiece,  how 
many  can  be  bought  for  20  dollars  ? 

5.  Mary  gave  36  cents  for  4  yards  of  rib- 
bon ;  how  much  was  it  a  yard  ? 

6.  If    4   benches   will    accommodate   24 
pupils,  how  many  must  sit  on  each  bench  ? 

7.  If  you  put  32  sheep  into  4  pens,  how 
many  must  you  put  into  each  pen  ? 

8.  Helen  paid  4  shillings  a  yard  for  lace  ; 
how  many  yards  could  she  buy  for  16  shil- 
lings ? 

9.  At  4  dimes  apiece,  how  many  books 
can  be  bought  for  24  dimes  ] 

10.  Carrie  gave  12  cents  for  4  skeins  of 
silk  ;  how  much  was  it  a  skein  ? 


DIVISION. 


53 


LESSON   V. 


5  in    5,  1  time 
5  in  10,  2  times 
5  in  15,  3  times 
5  in  20,  4  times 
5  in  25,  5  times 


5  in  30,  6  times 
5  in  35,  7  times 
5  in  40,  8  times 
5  in  45,  9  times 
5  in  50,  10  times 


1.  A  man  has  30  dollars,  which  he  wishes 
to  lay  out  in  flour  at  5  dollars  a  barrel ;  how 
many  barreK  can  he  buy  I 

2.  If  I  pay  10  cents  for  riding  5  miles  in 
the  cars,  how  much  is  that  a  mile  I 

3.  George   wishes   to    divide    15    apples 
among  5  boys ;  how  many  must  he  give  to 
each  1 

4.  In  a  school  of  35  pupils,  there  were  5 
classes  ;  how  many  pupils  in  a  class  ? 

5.  How  many  tons  of  coal,  at  5  dollars  a 
ton,  can  a  blacksmith  purchase  for  40  dol- 
lars ] 

6.  How  long  will  it  take  a  man  to  drive 
50  miles,  with  a  horse  and  carriage,  if  he 
drive  5  miles  an  hour  1 

•  7.  How  many  pounds  of  tea,  at  5  shillings 
a  pound,  can  be  bought  for  20  shillings  1 

8.  Henry  gave  45  cents  to  5  poor  chil- 
dren ;  how  many  cents  did  he  give  to  each 
child  I 


54 


DIVISION. 


LESSON   VI. 


6  in    6,  1  time 
6  in  12,  2  times 
6  in  18,  3  times 
6  in  24,  4  times 
6  in  30,  5  times 


6  in  36,  6  times 
6  in  42,  7  times 
6  in  48, 
6  in  54, 


8  times 

9  times 
6  in  60,  10  times 


1.  If  a  man  can  dig  48  rods  of  ditch  in 
6  days,  how  many  rods  can  he  dig  in  one 
day? 

2.  In  New  England,  6  shillings  make  one 
dollar ;  how  many  dollars  in  30  shillings  1 

3.  At  6  cents  a  pound,  how  many  pounds 
of  lard  can  be  bought  for  54  cents  1 

4.  Burton  sold  6  quarts  of  cherries  for  36 
cents ;  how  much  did  he  get  a  quart  1 

5.  If  a  man  build  42  rods  of  fence  in  6 
days,  how  many  rods  can  he  build  in  one 
day  I 

6.  How  long  will  it  take  you  to  read  60 
pages,  if  you  read  6  pages  a  day  1 

7.  If  6  bushels  of  rye  cost  6  dollars,  how 
much  is  that  a  bushel  ? 

8.  If  a  steamboat  run  6  miles  an  hour, 
how  long  will  it  take  her  to  run  24  miles  ? 

9.  When  crackers  are  6  cents  a  pound, 
how  many  pounds  can  be  bought  for   18 
cents  ] 


DIVISION.  55 


LESSON   VII. 


7  in    7,  1  time 
7  in  14,  2  times 
7  in  21,  3  times 
7  in  28,  4  times 
7  in  35,  5  times 


7  in  42,  6  times 
7  in  49,  7  times 
7  in  56,  8  times 
7  in  63,  9  times 
7  in  70,  10  times 


1.  How  many  yards  of  cloth,  at  7  shillings 
a  yard,  can  be  bought  for  42  shillings  ? 

2.  A  farmer  sold  7  sheep  for  14  dollars  ; 
how  much  did  he  receive  apiece  ? 

3.  Seth  sold  his  sled  for  35  cents;  how 
many  slates,  at  7  cents  apiece,  can  he  buy 
for  the  money  I 

4.  If  7  yards  of  calico  will  make  a  dress, 
|  how  many  dresses  can  be  made  from  a  piece 
j  containing  28  yards  1 

5.  In  one  week  there  are  7  days;    how 
many  weeks  in   21  days?   in  28  days'?   in 
56  days  ?   in  70  days? 

6.  Levi  paid  7  cents  for  7  slate  pencils ; 
how  much  did  he  pay  apiece  ] 

7.  If  a  man  can  build  49  rods  of  stone 
wall  in  7  days,  how  much  can  he  build  in 
1  day] 

8.  When  hops  are  7  centa  a  pound,  how 
many  pounds  can  be  bought  for  70  cents  ? 

9.  How  many  times  7  in  63  ? 


56 


DIVISION. 


LESSON   VIII. 


Sin  8, 
8  in  16, 
8  in  24, 
8  in  32, 


1  time 

2  times 

3  times 

4  times 


8  in  80,  10  times 


8  in  48, 
8  in  56, 
8  in  64, 

8  in  72, 


6  times 

7  times 

8  times 

9  times 


8  in  40,    5  times 


1.  Giles  can  buy  a  hoop  for  8  cents;  how 
many  hoops  can  he  buy  for  40  cents  ? 

2.  A  man  paid  72  cents  for  8  pounds  of 
sugar ;  what  was  the  price  of  one  pound  ? 

3.  How  many  bins  will   be  required   to 
hold  56  bushels  of  oats,  if  each  bin  hold  8 
bushels  1 

4.  At  8  dollars  a  ton,  how  many  tons  of 
hay  can  be  bought  for  64  dollars  ? 

5.  A  farmer  sold  8  barrels  of  apples  for 
24  dollars ;  how  much  did  he  receive  for  one 
barrel  1 

6.  If  there  are  8  trees   in  each  row,  how 
many  rows  are  there  in  an  orchard  contain- 
ing 80  trees  ? 

7.  How  many  spelling  books,  at  8  cents 
apiece,  can  you  buy  for  48  cents  ? 

8.  A   laborer   received    16   dollars  for  8 
days'  work ;  how  much  was  that  a  day  ? 

9.  James  bought  8  lemons  for  32  cents ; 
what  was  the  cost  of  one  lemon  ? 


DIVISION.                                         57 

LESSON    IX. 

9  in    9,  1  time 

9  in  54,    6  times 

9  in  18,  2  times 

9  in  63,    7  times 

9  in  27,  3  times 

9  in  72,    8  times 

9  in  36,  4  times 

9  in  81,    9  times 

9  in  45,  5  times 

9  in  90,  10  times 

1.  How  many  classes,  of  9  pupils  each, 
can  be  formed  of  45  pupils  \ 

2.  When  eggs  are  9  cents  a  dozen,  how 
many  dozen  can  be  bought  for  63  cents  ? 

3.  A  class  of  9  pupils  present  their  teacher 
with   a  book   which   cost   90   cents ;    how 
many    cents    must    each  pay    towards    the 
book] 

4.  If  you  travel  9  miles  an  hour,  how  long 
will  it  take  you  to  travel  81  miles  ? 

5.  A  farmer  distributed  9  bushels  of  pota- 
toes equally  among  9  poor  families;    how 
many  did  he  give  to  each  \ 

6.  If  a  man  spend  9  cents  a  day  for  cigars, 
how  long  will  54  cents  last  him  ? 

7.  For  72  shillings,  how  many  yards  of 
silk  can  a  lady  buy  at  9  shillings  a  yard  I 

8.  William  sold  9  quarts  of  cherries  for 
36  cents ;  how  much  did  he  receive  a  quart  ? 

9.  How  many  tons  of  hay,  at  9  dollars  a 
ton,  can  be  bought  for  18  dollars  \ 


58 


DIVISION. 


LESSON   X. 

10  in    60,  6  times 

10  in    70,  7  times 

10  in    80,  8  times 

10  in    90,  9  times 


10  in  10,  1  time 

10  in  20,  2  times 

10  in  30,  3  times 

10  in  40,  4  times 

10  in  50,  5  times 


10  in  100,  10  times 


1.  When  butter  is  10  cents  a  pound,  how 
many  pounds  can  I  buy  for  80  cents  ? 

2.  At  10  dollars  an  acre,  how  many  acres 
of  land  can  be  bought  for  100  dollars  I 

3.  How  long  will  it  take  a  boy  to  earn  90 
cents,  if  he  earn  10  cents  a  day? 

4.  In  one  dime  are  10  cents;  how  many 
dimes  in  30  cents  ? 

5.  At  10  shillings  apiece,  how  many  glass 
lamps  can  be  bought  for  50  shillings  ? 

6.  How  long  will  it  take  you  to  read  70 
pages,  if  you  read  10  pages  a  day  ? 

7.  When  shawls  are  10  dollars  apiece,  how 
many  can  be  bought  for  60  dollars  ? 

8.  How  long  will  it  take  you  to  earn  40 
dollars,  if  you  earn  10  dollars  a  month'? 

9.  If  one  man  can  build  10  rods  of  fence 
in  one  day,  how  many  men  will  it  take  to 
build  20  rods  in  the  same  time  1 

10.  At  10  cents  apiece,  how  many  melons 
can  be  bought  for  40  cents  ? 


DIVISION.                                         59 

LESS( 

PROMISCUOl 

6  in  36,  how  many  times  ? 
7  in  42,  how  many  times  ? 
6  in  18,  how  many  times  ? 
9  in  81,  how  many  times  ? 
5  in  35,  how  many  times  ? 
8  in  72,  how  many  times  ? 
9  in  27,  how  many  times  ? 
4  in  20,  how  many  times  ? 
3  in  18,  how  many  times  ? 
6  in  54,  how  many  times  ? 

3N    XI. 

US    REVIEW. 

3  in  15,  how  many  times? 
5  in  25,  how  many  times? 
9  in  63,  how  many  times  ? 
6  in  12,  how  many  times? 
7  in  28,  how  many  times? 
4  in  16,  how  many  times? 
7  in  49,  how  many  times  ? 
4  in  36,  how  many  times? 
8  in  64,  how  many  times  ? 
8  in  40,  how  many  times  ? 

8  in  24,  how  many  times  ? 
5  in  45,  how  many  times  ? 
6  in  42,  how  many  times? 
8  in  56,  how  many  times? 
9  in  18,  how  many  times? 
5  in  40,  how  many  times  ? 
7  in  63,  how  many  times  ? 
3  in  27,  how  many  times  ? 
7  in  21,  how  many  times? 
8  in  16,  how  many  times  ? 

3  in  12,  how  many  times  ? 
4  in  28,  how  many  times  ? 
8  in  32,  how  many  times  ? 
6  in  48,  how  many  times  ? 
2  in  14,  how  many  times? 
9  in  45,  how  many  times  ? 
8  in  48,  how  many  times  ? 
7  in  56,  how  many  times  ? 
3  in  21,  how  many  times  ? 
6  in  54,  how  many  times  ? 

8  in    8,  how  many  times? 
4  in  12,  how  many  times? 
7  in  35,  how  many  times? 
5  in  10,  how  many  times? 
7  in  14,  how  many  times? 
2  in     6,  how  many  times? 
4  in  24,  how  many  times? 
5  in  30,  how  many  times? 
9  in  36,  how  many  times? 
6  in  30,  how  many  times? 

3  in  24,  how  many  times? 
2  in  16,  how  many  times? 
4  in  32,  how  many  times? 
6  in  24,  how  many  times? 
9  in  72,  how  many  times? 
5  in  10,  how  many  times? 
4  in     8,  how  many  times  ? 
5  in  20,  how  many  times? 
2  in  10,  how  many  times? 
7  in     7,  how  many  times? 

60  DIVISION. 


LE  S  S  ON.  XI  I. 

PROMISCUOUS  EXAMPLES. 

1.  When  flour  is  7  dollars  a  barrel,  how 
many  barrels  can  be  bought  for  63  dollars  ? 

ANALYSIS.  —  Since  7  dollars  will  buy  1  barrel,  G3 
dollars  will  buy  as  many  barrels  as  7  dollars,  the  price 
of  1  barrel,  is  contained  times  in  63  dollars,  which  are 
9  times.  Therefore,  fyc. 

2.  If  it  take  81  bushels  of  apples  to  make 
9  barrels  of  cider,  how  many  bushels  will 
make  one  barrel "? 

3.  How  long  will  it  take  5  men  to  do  a 
job  of  work  that  one  man  can  do  in  30  days  I 

4.  How  long  will  12  dollars  pay  for  my 
board,  at  the  rate  of  6  dollars  a  week  I 

5.  If  54  pounds  of  provision  last  one  man 
9  days,  how  many  pounds  would  last  him 
one  day  ? 

6.  Marcus  read   100  pages  in  10  days; 
how  many  pages  did  he  read  each  day  1 

7.  A  cabinet  maker  received  45  dollars  for 
some  chairs  at  5  dollars  apiece ;  how  many 
chairs  did  he  sell  1 

8.  Jf  one  man  can  mow  a  field  of  grass  in 
18  days,  in  what  time  would  6  men  mow  the 
same  I 

9.  A  farmer  sold  some  hay  for  30  dollars, 
and  took  10  sheep  for  payment;  what  was 
the  cost  of  each  sheep  ? 


PKOMISCUOUS   REVIEW.  61 

LESSON    XIII. 

1.  How  many  tons  of  hay,  at  6  dollars  a 
ton,  will  pay  for  8  yards  of  broadcloth,  at  3 
dollars  a  yard  ? 

ANALYSTS.  —  As  many  tons  of  hay  at  6  dollars  a  ton, 
as  6  dollars,  the  price  of  a  ton,  is  contained  times  in 
8  times  3  dollars,  or  24  dollars,  the  cost  of  the  broad- 
cloth, which  are  4  times.  Therefore  4  tons  of  hay,  at 
6  dollars  a  ton,  will  pay  for  8  yards  of  broadcloth,  at  3 
dollars  a  yard. 

2.  How  many  dozen  of  eggs,  at  9  cents  a 
dozen,  will  pay  for   6  yards  of  calico,  at  6 
cents  a  yard  I 

3.  Charles  sold  6  quarts  of  beech  nuts,  at 
4  cents  a  quart,  and  took  his  pay  in  oranges, 
at  3  cents  apiece ;  how  many  oranges  did  he 
receive  ] 

4.  At  6  dollars  a  barrel,  how  many  bar- 
rels of  flour  will  pay  for  3  barrels  of  pork, 
at  10  dollars  a  barrel  ? 

5.  If  5  men  can  hoe  a  field  of  corn  in  6 
days,  how  long  will  it  take  one  man  ? 

6.  If  8  men  can  build  a  shed  in  10  days, 
how  many  men  must  be  employed  to  build  it 
in  one  day  ? 

7.  If  4  men  can  do  a  piece  of  work  in  7 
days,  how  long  will  it  take  one  man  to  do  it  I 

8.  How  many  days'  labor,  at  8  shillings 
a  day,  will  pay  for  10  bushels  of  potatoes  at 
4  shillings  a  bushel  ? 


62  PROMISCUOUS   REVIEW. 


LESSON    XIV. 

1.  If  7  oranges  cost  28  cents,  what  will  3 
oranges  cost  ] 

ANALYSIS.  —  If  7  oranges  cost  28  cents,  1  orange 
will  cost  as  mang  cents  as  7  is  contained  times  in  28, 
which  is  4  times  ;  3  oranges,  which  are  3  times  1  orange, 
will  cost  3  times  4  cents,  or  12  cents.  Therefore,  if  7 
oranges  cost  28  cents,  3  oranges  will  cost  12  cents. 

2.  If  6  pounds  of  sugar  cost  60  cents, 
what  will  9  pounds  cost  ? 

3.  A  farmer  sells  8  sheep  for  24  dollars ; 
how  much  does  he  receive  for  5  sheep  ? 

4.  If  a  man   can   earn   72  dollars  in    8 
weeks,  how  much  can  he  earn  in  10  weeks  ? 

5.  Jane  bought  5  steel  pens  for  15  cents ; 
what  would  be  the  cost  of  10  pens  at  the 
same  rate  ? 

6.  A  grocer  sold  10  pounds  of  tea  for  40 
shillings;    what   would   be   the   cost   of  8 
pounds  at  the  same  rate  ? 

7.  If  a  man  can  chop  16  cords  of  wood  in 
8  days,  how  much  can  he  chop  in  3  days  1 
in  5  days'?   in  7  days?    in  10  days'?    in  12 
days  ? 

8.  If  7  yards  of  calico  cost  63  cents,  what 
will    3    yards    cost?    5  yards'?    6  yards'?    9 
yards]  10  yards  ? 

9.  When  4  cords  of  wood  are  worth  20 
dollars,  what  will  9  cords  be  worth  *? 


PROMISCUOUS   REVIEW.  63 

LESSON    XV. 

1.  Isabel  had   15   pinks,  and  gave  6  to 
Clara,  and  4  to  Herbert ;  how  many  did  she 
keep  for  herself? 

ANALYSIS.  —  She  kept  as  many  pinks  as  the  difference 
between  15  pinks  and  the  sum  of  6  pinks  and  4  pinks  ; 
6  and  4  are  10,  and  10  from  15  leaves  5.  Therefore, 
if  Isabel  had  15  pinks,  and  gave  away  10,  she  had  5  left. 

2.  Lucian,  having  20  marbles,  gave  9  to 
Henry,  and  6  to  John ;  how  many  had  he 
left? 

3.  From  a  piece  of  cloth  containing  12 
yards,  5  yards  were  cut  for  a  coat,  3  yards 
for  a  pair  of  pantaloons,  and  1  yard  for  a 
vest ;  how  many  yards  were  left  ? 

4.  If  2  men  start  from  the  same  place  and 
travel  in  opposite  directions,  one  at  the  rate  of 

4  miles  an  hour,  and  the  other  at  the  rate  of 

5  miles  an  hour,  how  far  apart  will  they  be 
at  the  end  of  1  hour  ?   At  the  end  of  2  hours  I 
5  hours'?  6  hours'?  8  hours'?  10  hours'? 

5.  A  grocer  sold  2  pounds  of  rice  at  6 
cents  a  pound,  a  pound  of  soda  for  8  cents, 
and  a  bar   of  soap   for    7   cents,  and  was 
paid  in  eggs  at  9  cents  a  dozen;  how  many 
dozen  of  eggs  did  he  receive  ? 

6.  If  a  man  travel  36  miles  in  9  hours, 
how  far  will  he  travel  in  5  hours'?    in  6 
hours  1  in  7  hours  1 


64 


FRACTIONS. 


LESSOR    I. 

When  a  unit  or  whole  thing  is  divided  into  two  or 
more  equal  parts,  those  parts  are  called  FRACTIONS. 

1.  If  a  yard  measure  be  divided  into  two  equal  parts, 
one  of  the  parts  is  called  one  half. 


How  many  halves  make  a  whole  thing  ?     Ans.  Two. 

2.  If  a  yard  measure  be  divided  into  three  equal 
parts,  one  of  the  parts  is  called  one  third, 

How  many  thirds  make  a  whole  thing  ?     Ans.  Three. 

3.  If  a  yard  measure  be  divided  into  four  equal  parts, 
one  of  the  parts  is  called  one  fourth,  two  of  the  parts 
two  fourths,  three  of  the  parts  three  fourths. 


D  N E  FOU  R TH .    I  iO'NE  F..O U  R.T H          ON E  FO  0  RT H 


How  many  fourths  make  a  whole  thing?  Ans. 
Four. 

4.  If  a  yard  measure  be  divided  into  five  equal  parts, 
one  of  the  parts  is  called  one  fifth,  two  of  the  parts 
two  fifths,  three  of  the  parts  three  fifths,  four  of  the  parts 
four  fifths. 


How  many  fifths  make  a  whole  thing?     Ans.   Five. 

5.  If  a  yard  measure  be  divided  into  six  equal  parts, 
one  of  the  parts  is  called  one  sixth,  two  of  the  parts  two 
sixths,  and  so  on. 


OHE/SIXTRJ  :ONE,S!XTH     ONES1XTH      ONE  SIXTH 


How  many  sixths  make  a  whole  thing  ?     Ans.  Six. 


FRACTIONS.  65 


LESSON    II. 

1.  If  any  number  or  whole  thing  be  divided 
into  seven  equal  parts,  one  of  the  parts  is 
called   one   seventh,   two   of  the  parts   two 
sevenths,  and  so  on. 

How  many  sevenths  make  a  whole  thing  ? 
Ans.  Seven  sevenths. 

2.  If  any  number  or  thing  be  divided  into 
eight  equal  parts,  one  of  the  parts  is  called 
one  eighth,  five  of  the  parts  Jive  eighths,  and 
so  on. 

How  many  eighths  make  a  whole  thing  ? 
Ans.  Eight  eighths. 

3.  If  any  number  or  thing  be  divided  into 
nine  equal  parts,  one  of  the  parts  is  called 
one  ninth,  seven  of  the  parts  seven  ninths, 
and  so  on. 

How  many  ninths  make  a  whole  thing? 
How  many  tenths  make  a  whole  thing? 
The  following  is  the  method  of  expressing 
fractions  by  figures :  — 


i,  one  half. 
I,  one  third, 
i,  one  fourth. 


I,  one  fifth. 
4,  one  sixth. 
I,  one  seventh. 


\  ,  one  eighth, 
i ,  one  ninth. 
T\T,  one  tenth. 


NOTE.  —  In  any  fraction,  as  §,  (two  thirds,),  the  num- 
ber below  the  line  is  called  the  Denominator,  and  it 
shows  into  how  many  equal  parts  the  whole  number  or 
thing  is  divided.  The  number  above  the  line  is  called 
the  Numerator,  and  it  shows  the  number  of  parts  that 
are  used,  or  that  are  expressed  by  the  fraction. 


66  FRACTIONS. 


LESSON    III. 

1.  What  do  you  understand  by  i  of  any 
number  or  thing  ? 

Ans.  One  of  the  two  equal  parts  into  which 
the  number  or  thing  is  divided. 

2.  What  do  you  understand  by  I  of  any 
number  or  thing] 

Ans.   One  of  the  three  equal  parts  into 
which  the  number  or  thing  is  divided. 

3.  What  do  you  understand  by  %  of  any 
number  or  thing] 

Ans.   Two  of  the  three  equal  parts  into 
which  the  number  or  thing  is  divided. 

4.  How  do  you  find  £  of  any  number? 
Ans.    Divide  the  given  number  by  2. 

5.  How  do  you  find  i  of  any  number? 
Ans.  Divide  the  given  number  by  3. 

6.  How,  then,  will  you  find  i  of  any  num- 
ber ?    how  i  ?    how  I  ?   how  I  ?  how  £  ?  how 


7.  What  do  you  understand  by  i  of  any 
number  or  thing  ?  by  f  ?  by  f  ?  by  f  ?  by  i  ? 
byf?  byj?  byil'byt?  byt?  byH  by*? 
byH 

9.  What  is  i  of  4?    of  6?    of  8?  of  10? 
of  16?   of  20? 

10.  What  is  i  of  8?  of  12?  of  16?  of  20? 
of  28? 

11.  What  is  i  of  12?   of  24?   of  36? 


FRACTIONS.  67 


LESSON   IV. 

1.  In  1  orange,  how  many  halves? 

2.  In  3  oranges,  how  many  halves  ? 

ANALYSIS.  —  Since  in  1  orange  there  are  2  halves,  in 
3  oranges  there  are  3  times  2  halves,  which  are  6  halves. 
Therefore,  in  3  oranges  there  are  6  halves. 

3.  How  do   you   find  how  many  halves 
there  are  in  any  number  or  thing  ? 

Ans.  Multiply  the  whole  number  by  2. 

4.  How  do   you   find  how  many   thirds 
there  are  in  any  number  or  thing  ? 

Ans.  Multiply  the  whole  number  by  3. 

5.  How  many  halves  are  there  in  4  pears  ? 
in  4  pears  and  1  half  ?  in  5  pears  ? 

6.  In  6  bushels  and  1  half,  how  many 
halves  ? 

7.  In  3  apples,  how  many  thirds  ? 

8.  In  4  apples  and  1  third,  how  many 
thirds  are  there  ?  in  4  and  2  thirds  ?  in  5  ? 
in  5  and  1  third  ? 

9.  How  many  halves  in  7  ?   in  7  and  1 
half?  in  8?  in  9  and  1  half?  in  10? 

10.  How  many  thirds  in  5  ?  in  5  and  1 
third  ?  in  5  and  2  thirds  ?   in  6  ?   in  7  and 
1  third?   in  7  and  2  thirds? 

11.  In  8  dollars,  how  many  halves?  how 
many  thirds  ? 

12.  How  many  half  miles,  in  7  miles  and 
1  half? 


68  FRACTIONS. 


LESSON    V. 

1.  In  5  bushels,  how  many  fourths  ? 

ANALYSIS.  —  Since  in  1  bushel  there  are  4  fourths, 
in  5  bushels  there  are  5  times  4  fourths,  which  are  20 
fourths.  Therefore,  in  5  bushels  there  are  20  fourths. 

2.  How  many  fourths  in  6  ?  in  6  and  1 
fourth?    in  6  and  3  fourths?    in  7  and  1 
fourth  1  in  8  and  3  fourths  ?   in  9  ? 

3.  How  many  fifths  in  2  ?  in  3  ?  in  4  and 
1  fifth  ?  in  5  and  2  fifths  ?  in  7  and  3  fifths  ? 

4.  How  many  sixths  in  1  ?   in  2  ?   in  4  ? 
in  4  and  1  sixth?  in  7  and  2  sixths?  in  7 
and  5  sixths  ? 

5.  In  3,  how  many  sevenths  ?  in  3  and  5 
sevenths  ?  in  4  and  1  seventh  ?  in  4  and  4 
sevenths  ? 

6.  In  7,  how  many  sevenths  ?  in  7  and  6 
sevenths  ? 

7.  How  many  eighths  in  2  ?  in  3  ?  in  5 
and  1  eighth  ?  in  5  and  7  eighths  ? 

8.  In  1,  how  many  ninths  ?  in  2 1  in  5  ? 
in  6  ?  in  4  and  3  ninths  ?  in  7  and  5  ninths  ? 
in  8? 

9.  How  many  tenths  in  1  ?  in  2  ?  in  3  ? 
in  4  and  5  tenths  ?  in  6  and  3  tenths  ?   in  9 
and  9  tenths  ? 

10.  In  6,  how  many  fifths  ?   how  many 
sixths?    how   many    sevenths?    how   many 
eighths  ?  how  many  ninths  ? 


FRACTIONS.  69 


LESSON   VI. 

1.  In  6  halves  of  a  mile,  how  many  miles  ? 

ANALYSIS.  —  Since  there  are  2  halves  in  1  mile,  in  6 
halves  of  a  mile  there  are  as  many  miles  as  2  halves 
are  contained  times  in  6  halves,  which  are  3  times. 
Therefore,  in  6  halves  of  a  mile  are  3  miles. 

2.  How  many  bushels  in  14  halves  of  a 
bushel  ? 

3.  In  12  halves,  how  many  units  or  whole 
ones? 

4.  How  many  units  in  15  thirds?  in  18 
thirds?  in  21  thirds? 

5.  How   many  units   in   16  fourths?   in 
17  fourths?   in  18  fourths?   in  20  fourths? 
in  23  fourths  ? 

6.  In  7  fifths,  how  many  whole  ones  ?  in 
10  fifths?   in  25  fifths  ?   in  26  fifths?  in  28 
fifths? 

7.  How  many  times  1  in  18  sixths  ?  in  19 
sixths  ?   in  24  sixths  ?   in  30  sixths  ?   in  32 
sixths  ? 

8.  In  f  how  many  times  1  ?   in  -V1  ?    in  V- 

9.  How  many  times  1  in  I  ?    in  Y  ?   in 
-^  ?  in  *8-  ?  in  V-  ?  in  %4  ?  in  -3/-  ? 

10.  How  many  units  in  £?  in  -V0-?   in  -^? 
inV-?in^?  in%7-? 

11.  In  -B,  how  many  times  1  ?   in  f*?   in 
f*?  inH?  in^?  intt?  ii 


70  FRACTIONS. 


LESSON   VII. 

1.  George  had  f  of  a  dollar,  and  his  father 
gave  him  t  of  a  dollar  more ;  what  part  of  a 
dollar  had  he  then  1 

ANALYSIS.  —  He  had  the  sum  of  f  of  a  dollar  and  f 
of  a  dollar  ;  f  and  f  make  f  of  a  dollar.  Therefore, 
since  George  had  §  of  a  dollar,  and  his  father  gave  him 
g  of  a  dollar  more,  he  then  had  %  of  a  dollar. 

2.  A  lady  gave  f  of  an  orange  to  Mary,  f 
to  Sarah,  and  ?  to  Julia ;  how  many  oranges 
did  she  give  away  ? 

3.  John  bought  i  of  a  pound  of  raisins, 
and  Joseph  f  of  a  pound ;  how  many  pounds 
did  they  both  buy  I 

4.  A  blacksmith  bought  at  one  time  f  of 
a  ton  of  coal,  at  another  time  f  of  a  ton,  at 
another  time  t  of  a  ton,  and  at  another  time 
i  of  a  ton ;  how  many  tons  did  he  buy  in  all  1 

5.  Samuel  paid  T%  of  a  dollar  for  a  slate, 
A  of  a  dollar  for  an  arithmetic,  -TV  for  a 
reader,  and  T9<y  for  a  geography  and  atlas; 
how  many  dollars  did  he  pay  for  all  ? 

6.  A  man  chopped  f  of  a  cord  of  wood  in 
the  forenoon,  and  I  of  a  cord  in  the  after- 
noon ;  how  much  did  he  chop  in  a  day  ? 

7.  In  the  sum  of  f  and  f  and  f  and  f ,  how 
many  whole  ones  ? 

8.  In  the  sum  of  i  and  $  and  f  and  f ,  how 
many  whole  ones  ? 


FRACTIONS.  71 


LESSON    VIII. 

1.  A  gentleman,  having  i  of  an  acre  of 
land,  sold  f  of  an  acre ;  what  part  of  an  acre 
had  he  left  ? 

ANALYSIS.  —  He    ad  left  the  difference  between  F  of 
an  acre  and  £  of  an  acre,  which  is  f  of  an  acre.     There- 
fore, since  a  gentleman  had  £  of  an  acre  of  land,  and 
I   sold  f  of  an  acre,  he  had  f  of  an  acre  left. 

2.  Frank  spent  %  of  his  money,  and  lost  f 
of  it ;  what  part  of  his  money  had  he  left  ? 

3.  Oscar  bought  a  pair  of  skates  for  TTU  of  a 
dollar,  and  sold  them  for  A  of  a  dollar ;  how 
much  did  he  gain  by  his  bargain  ] 

4.  Eugene  owns  f  of  a  kite,  and  Herbert 
the  remainder;  what  part  of  the  kite  does 
Herbert  own  ? 

5.  Clara,  having  a  quire  of  paper,  gave  i 
of  it  to  Emeline,  and  f  to  Caroline ;  what 
part  did  she  keep  for  herself? 

6.  If  I  divide  an  orange  into  5  equal  parts, 
and  give  away  3  pieces,  what  part  of  the 
orange  will  be  left  ? 

7.  A  barrel  of  flour  was  distributed  among 
three  poor  families ;  the  first  received  f  of  a 
barrel,   the   second  f-  of  a  barrel,  and  the 
third  the  remainder ;  what  part  of  a  barrel 
did  the  third  receive  ? 

8.  A-  and  T3<y  and  -&  less  iV,  are  how  many 
tenths  ? 


72  FRACTIONS. 


LESSON    IX. 

1.  5  is  £  of  what  number  ] 

ANALYSIS. —  5  is  1  half  of  2  times  5,  which  are  10. 
Therefore,  5  is  1  half  of  10. 

2.  3  is  i  of  what  number  ] 

3.  6  is  i  of  what  number  ? 

4.  7  is  i  of  what  number  ? 

5.  5  is  i  of  what  number  ] 

6.  9  is  i  of  what  number  ? 

7.  8  is  |  of  what  number  ? 

8.  4  is  yV  of  what  number  ? 

9.  2  is  i  of  what  number  1 

10.  A  man  bought  i  of  a  cord  of  wood 
for  2  dollars ;  how  much  will  a  cord  cost,  at 
the  same  rate  ? 

11.  If  i  of  a  pound  of  coffee  cost  4  cents, 
what  will  a  pound  cost  1 

12.  A  lady  paid  10  cents  for  &  of  a  yard 
of  silk  ?  how  much  must  she  pay  for  a  yard  ] 

13.  Homer   gave   6   cents   to   a   beggar, 
which  was  i  of  all  he  had ;  how  many  cents 
had  he  at  first  ? 

14.  A  farmer  received  5  dollars  towards 
the  payment  for  a  horse,  which  was  £  of 
what  he  sold  him  for ;  what  was  the  price 
of  the  horse  ? 

15.  James  sold  a  kite  for  4  cents  more 
than  it  cost  him,  and  gained  just  |  of  what 
he  gave  for  it ;  what  did  it  cost  ? 


FRACTIONS.  73 


LESSON   X. 

1.  Lester  bought  i  of  a  pound  of  raisins 
for  5  cents ;  what  would  £  of  a  pound  cost, 
at  the  same  rate  I 

ANALYSIS.  —  Since  1  fourth  of  a  pound  of  raisins 

cost  5  cents,  3  fourths  of  a  pound,  which  are  3  times  1 

fourth^  will  cost  3  times  5  cents,  which  are  15  cents. 

Therefore,  since  %  of  a  pound  of  raisins  cost  5  cents, 

%  of  a  pound  will  cost  15  cents. 

2.  If  i  of  an  acre  of  land  cost  6  dollars, 
what  will  f  of  an  acre  cost,  at  the  same  rate  ? 

3.  There  are  5  yards  in  i  of  a  piece  of 
cloth ;  how  many  yards  in  f  of  the  piece  ?  in 
t  of  the  piece  I  in  the  whole  piece  1 

4.  If  i  of  a  barrel  of  flour  cost  2  dollars, 
what  will  f  of  a  barrel  cost  ?  what  will  f 
cost  ?  what  will  the  whole  barrel  cost  ? 

5.  If  i  of  a  bushel  of  walnuts  cost  3  shil- 
lings, what  will  f  of  a  bushel  cost  ?   what 
will  a  bushel  cost  ? 

6.  Paid  2  dollars  for  i  of  a  ton  of  hay ; 
what  would  be  the  cost  of  a  ton,  at  the  same 
rate? 

7.  A  man  spent  9  dollars  in  i  of  a  month  ; 
how  much  would  he  spend  in  £  of  a  month, 
at  the  same  rate  ?  how  much  in  a  month  ? 

8.  In -iV  of  a  dollar  are   10  cents;  how 
many  cents  in  T4u  of  a  dollar  ]  in  A  ?  in 

in  a  whole  dollar  ] 


74  FRACTIONS. 


LESSON    XI. 

1.  If  a  man  earn  i  dollar  in  one  day,  how 
many  dollars  will  he  earn  in  6  days  ? 

ANALYSIS. — If  a  man  earn  1  half -dollar  in  1  day, 
in  6  days,  which  are  6  times  1  day,  he  will  earn  6 
times  %  dollar,  or  6  halves  of  a  dollar,  equal  to  3  dollars. 
Therefore,  if  a  man  earn  %  dollar  in  1  day,  in  6  days 
he  will  earn  3  dollars. 

2.  How  many  are  5  times  f  ? 

3.  How  many  are  6  times  t  ? 

4.  How  many  are  7  times  I  ? 

5.  How  many  are  8  times  T^? 

6.  When  com  is  f  of  a  dollar  a  bushel, 
what  will  4  bushels  cost  ? 

7.  At  J-  of  a  dollar  a  pound,  what  will  5 
pounds  of  tea  cost  ? 

8.  Gave  I  of  a  bushel  of  corn  apiece  to  6 
poor  families ;  how  many  bushels  did  all  re- 
ceive ? 

9.  At  f  of  a  dollar  a  yard,  what  will  8 
yards  of  silk  cost  ? 

10.  When  peaches  are  T9u  of  a  dollar  a 
basket,  what  will  be  the  cost  of  7  baskets  ? 

11.  If  a  family  consume  ^  of  a  pound  of 
butter  a  day,  how  much  will  they  consume 
in  10  days  ? 

12.  Melville  gave  T2o  of  a  dollar  for  a  pair 
of  gloves,  and  7  times  as  much  for  a  hat; 
what  was  the  cost  of  his  hat  I 


FRACTIONS.  75 


LESSON   XII. 

1.  What  will  i  of  a  yard  of  cloth  cost,  at  6 
dollars  a  yard  ? 

ANALYSIS.  —  Since  3  thirds,  or  1  yard,  of  cloth  cost  6 
dollars,  I  third  of  a  yard  will  cost  %  of  6  dollars,  or  2 
dollars.  Therefore,  since  1  yard  of  cloth  cost  6  dollars, 
^  of  a  yard  will  cost  2  dollars. 

2.  At  12  cents  a  pound,  what  will  i  of  a 
pound  of  coffee  cost  I 

3.  When  hay  is  10  dollars  a  ton,  what 
will  be  the  cost  of  %  of  a  ton  ?    of  i  I    of  f  ? 
oft? 

4.  In  one  day  are  24  hours;  how  many 
hours  in  i  of  a  day?    in  i  of  a  day?   in  I ? 
in  f  ?   in  i  ? 

5.  Horace  is  28  years  old,  and  i  of  his  age 
is  just  the  age  of  his  younger  brother;  what 
is  the  age  of  his  brother  ? 

6.  Bought  a  piece  of  land  containing  48 
acres ;  how  many  acres  in  4  of  it  ?   in  I  of 
it  ?   in  I  of  it  ? 

7.  Gave  36  dollars  for  a  pile  of  wood; 
what  will  be  the  cost  of  i  of  it  ?  of  £  ?  of  i  ? 
of*?    off? 

8.  A  gentleman  spent  9  years  in  travel- 
ing; £  of  the  time  he  spent  in  the  United 
States,  and  the  remainder  in  Europe;  how 
many  years  did  he  spend  in  Europe  ? 


76 


TABLES. 


TABLES  OF  MONEY. 


UNITED   STATES  MONEY. 

United  States  money  is  the  legal  currency  of  the 
United  States. 

TABLE. 

10  mills  (m.)                  make  1  cent,  marked            ct. 

10  cents                               "    1  dime,  "                   d. 

10  dimes,  or  100  cents,      "    1  dollar,  "      doll,  or  $. 

10  dollars                           "    1  eagle,  "                 E. 

PARTS    OF    ONE    DOLLAR. 

The  following  table  gives  the  aliquot  parts  of  a 
dollar  in  United  States  money,  and  also  the  other  frac- 
tional parts  of  a  dollar  in  common  use. 


TABLE. 


of  a  doll, 
of  a  doll, 
of  a  doll, 
of  a  doll. 
=  £  of  a  doll, 
of  a  doll, 
of  a  doll. 


25 


50 


cents  ~  £  of  a  doll. 

cents  =  $  of  a  doll. 

cents  =  f  of  a  doll. 

cents  =  £  of  a  doll. 


62£  cents  =  |  of  a  doll. 
75  cents  =  f  of  a  doll. 
87£  cents  =  J  of  a  doll. 


ENGLISH   MONEY. 
English  money  is  the  legal  currency  of  Great  Brittain. 

TABLE. 

4  farthings  (qr.  or  far.)    make  1  penny, 
12  pence  "     1  shilling, 

20  shillings  "     1  pound, 

20  shillings  "      1  sovereign, 

An  English  shilling  =  241-  cents. 


marked    d. 
sov. 


« 


TABLES.  77 


TROY  WEIGHT.       '„,/  ; 

Troy  weight  is  used  in  weighing  g'^lcj,  spTf-JV  anrl 
jewels.  i* %  L 

TABLE. 

24  grains  (gr.)       make  1  pennyweight,  marked  pwt. 
20  pennyweights        "       1  ounce  "          oz. 

12  ounces  "      1  pound  "  Ib. 

AVOIRDUPOIS  WEIGHT. 

Avoirdupois  weight  is  used  in  weighing  almost  every 
kind  of  goods,  and  all  metals  except  gold  and  silver. 

TABLE. 

16  drams  (dr.)       make  1  ounce,  marked  oz. 

16  ounces  "  1  pound,  "        Ib. 

100  pounds  "  1  hundred  weight,       "     cwt. 

20  hundred  weight    "  1  ton,  «        T. 

NOTE.  —  A  pound  avoirdupois  is  heavier  than  a  pound  troy, 
but  an  ounce  troy  is  heavier  than  an  ounce  avoirdupois. 

5760  grains  troy  =  1  pound  troy. 

7000  grains  troy  =  1  pound  avoirdupois. 

175  pounds  troy  =  144  pounds         " 

175  ounces  troy  =  192  ounces         " 

APOTHECARIES'  WEIGHT. 

Apothecaries'  weight  is  used  in  mixing  medicines. 
But  medicines  are  always  bought  and  sold  by  avoirdu- 
pois weight. 

TABLE. 

20  grains  (gr.)  make  1  scruple,  marked  sc.  or  9. 

3  scruples  1  dram,  "       dr.  or    3. 

8  drams                  "  1  ounce,  "        oz.  or    §. 

12  ounces                 "  1  pound,  "         Ib.  or  Ib. 


78 


TABLES. 


The  follcwiaff  denominations  are  also  in  use : 

<  <  V  § 

56  pounds  make  ^1  firkin, of  butter. 

of  dried  salt  fish, 
of  raisins, 
of  flour. 

"   beef,  pork,  or  fish. 
"   salt  at  the  N.  Y.  salt  works. 
1  bushel  of 

oats, 
barley, 
corn  or  rye. 
wheat, 
clover  seed, 
beans. 

LIQUID   MEASURE. 
Wine  measure  is  used  to  measure  all  kinds  of  liquids. 


4    gills  (gi.)  make  1  pint, 

2    pints  "  1  quart, 

4    quarjff-  "—  1  gallon, 

Ulgallons    ~  "  1  barrel, 

2    barrels,  or  63  gals.    "  1  hogshead, 


marked  pt. 
qt. 
gal. 
bar. 
hhd. 


DRY   MEASURE. 


Dry  measure  is  used  to  measure  all  kinds  of  grain. 
2  pints  (pt.)  make  1   quart,  marked  qt. 

8  quarts  "      1  peck,  pk. 

4  pecks  "      1  bushel,  bu. 


BEER    MEASURE. 

"""  This  measure  is  rapidly  falling  into  disuse. 
2  pints  (pt).  make  1   quart, 

4  quarts  "       1   gallon, 

36  gallons  "       1   barrel, 

H  barrels,  or  54  gals.    "       1  hogshead 


marked  qt. 
«  gal. 
"  bbl. 
"  hhd. 


TABLES.  79 


SQUARE    MEASURE. 

Square  measure  is  used  for  measurjwg  surfaces. 
144  square  inches,  (sq.  in.)  make  1  fifJUAng  Focrt.  '.    {  ^  ;',', 

9  sojiare  feet  ^        "      1  square  yard! 

"S5J~square  "yaf3s  "      1  square  rod  or  perch. 

40  square  rods  or  perches     "      1  rood. 
4  roods  "      1   acre. 

640  acres  "      1  square  mile. 

CUBIC  MEASURE. 

Cubic  measure  is  used  for  measuring  solids. 
1728  cubic  inches  (cu.  in.)  make  1  cubic  foot,    mk'd  cu.  ft. 
27      "     feet  "     1      "     yard,      "  cu.yd. 

40  cu.  ft.  of  round  timber  or  )  n  ^ 

50   «     «     hewn       «  [  1  ton  or  load, 

24J  cubic  feet  make  1  perch  of  stone,  "      Pch. 

16     "      feet  "  •  1  cord  foot,         "      c.  ft. 

C. 


MEASURE. 

Long  measure  is  used  to  measure  distances. 
12  inches  (in.)  make  1  foot,  marked     ft. 

3  feet                               "     1  yard,  "  yd. 

ir^sVor  16j[J:eet      rt_  rrpjr^jupiole,  "  rd. 

ro3s                          """     llurlong,  "  fur. 

8  furlongs,  or  320  rods,  "     1  mile,  "  m. 

The  following  denominations  are  also  in  use. 

4  inches  make  1  hand. 
3  feei  /  "     1  pace. 

6  feet  A                         «  1  fathom. 

1.15  staJute  imles              "  1  geographical  mile. 

3  gaograpmbql  miles     "  1  league             marked  L. 

60  flreoprraphical^  )  -,    -,  -, 

69.16yLtntePmileS  %  1  deSree'  marked  deS'  or°' 

360^degrees                    \^"  a  great  circle  of  the  earth. 

=== 


80  TABLES. 


•-'•'     \J    MEASURE  OF  TIME. 

is- measure  is  applied  to  the  various  divisions  and 
•suMi  visions  of  time. 

60  seconds  (sec.)  make  1  minute,  marked  m. 

60  minutes  "  1  hour,  "  h. 

24  hours  "  1  day,  "  da. 

7  days  "      1  week,  «       w. 

4  weeks  "  1  lunar  month, "  mo. 

12  calendar  months,  or  3  65  days,  1  year,  "  yr. 

The  following  table  gives  the  names  of  the  12  calendar 
months^  in  their  order,  and  the  number  of  days  in  each. 

7.  July  has  31  days. 

8.  August          "31  days. 

9.  September    "  30  days. 

10.  October        "31  days. 

11.  November     "  30  days. 

12.  December     "31  days. 

CIRCULAR  MEASURE. 

Circular  Measure  is  applied  to  the  measurement  of  cir- 
cles and  angles,  and  is  used  in  reckoning  latitude  and  lon- 
gitude, and  the  revolutions  of  the  planets  round  the  sun. 
60  seconds  (")  make  1  minute,  marked  '. 

60  minutes  "     1  degree, 

30  degrees  "     1  sign, 

12  signs,  or  360  degrees  "    the  circle  of  the  Zodiac,  C. 

MISCELLANEOUS   TABLE. 

12  units  or  single  things  make  1  dozen. 

12  dozen,  or  144  units,  "  1  gross. 

12  gross,  or  144  dozen,  "  1  great  gross. 

20  units,  or  single  things,  1  score. 

24  sheets  of  paper  "  1  quire. 

20  quires  of  paper  "  1  ream. 


1.  January    has  31  days. 

2.  Februarys,"   28  days. 

3.  March        X31  days. 

4.  April          "   90  days. 

5.  May  «   31  days. 
7.  June  "   30  days. 


YA  0-1355 


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